kms states of quasi free dynamics on pimsner algebras abstract a continuous one parameter group of unitary isometries of a right hilbert c bimodule induces a quasi free dynamics on the cuntz pimsner c algebra of the bimodule and on its toeplitz extension the restriction of such a dynamics to the algebra of coefficients of the bimodule is trivial and the corresponding kms states of the toeplitz cuntz pimsner and cuntz pimsner c algebras are characterized in terms of traces on the algebra of coefficients this generalizes and sheds light onto various earlier results about kms states of the gauge actions on cuntz algebras cuntz krieger algebras and crossed products by endomorphisms we also obtain a more general characterization in terms of kms weights for the case in which the inducing isometries are not unitary and accordingly the restriction of the quasi free dynamics to the algebra of coefficients is nontrivial

cuntz krieger algebras of infinite graphs and matrices we show that the cuntz krieger algebras of infinite graphs and infinite 0 1 matrices can be approximated by those of finite graphs we then use these approximations to deduce the main uniqueness theorems for cuntz krieger algebras and to compute their k theory since the finite approximating graphs have sinks we have to calculate the k theory of cuntz krieger algebras of graphs with sinks and the direct methods we use to do this should be of independent interest

partial actions and kms states on relative graph c algebras abstract the relative graph c algebras introduced by muhly and tomforde are generalizations of both graph algebras and their toeplitz extensions for an arbitrary graph e and a subset r of the set of regular vertices of e we show that the relative graph c algebra c e r is isomorphic to a partial crossed product for an action of the free group generated by the edge set on the relative boundary path space given a time evolution on c e r induced by a function on the edge set we characterize the kms states and ground states using an abstract result of exel and laca guided by their work on kms states for toeplitz cuntz krieger type algebras associated to infinite matrices we obtain complete descriptions of the convex sets of kms states of finite type and of kms states of infinite type whose associated measures are supported on recurrent infinite paths this allows us to give a complete concrete description of the convex set of all kms states for a big class of graphs which includes all graphs with finitely many vertices

strongly self absorbing c algebras say that a separable unital c algebra v c is strongly self absorbing if there exists an isomorphism v such that lx ai e approximately unitarily equivalent homomorphisms we study this class of algebras which includes the cuntz algebras 2 ooo the uhf algebras of infinite type the jiang su algebra z and tensor products of 00 with uhf algebras of infinite type given a strongly self absorbing c algebra v we characterise when a separable c algebra absorbs v tensorially i e is p stable and prove closure properties for the class of separable testable c algebras finally we compute the possible if groups and prove a number of classification results which suggest that the examples listed above are the only strongly self absorbing c algebras

isomorphisms of algebras associated with directed graphs given countable directed graphs g and g we show that the associated tensor algebras open image in new window g and open image in new window g are isomorphic as banach algebras if and only if the graphs g are g are isomorphic for tensor algebras associated with graphs having no sinks or no sources the graph forms an invariant for algebraic isomorphisms we also show that given countable directed graphs g g the free semigroupoid algebras open image in new window and open image in new window are isomorphic as dual algebras if and only if the graphs g are g are isomorphic in particular spatially isomorphic free semigroupoid algebras are unitarily isomorphic for free semigroupoid algebras associated with locally finite directed graphs with no sinks the graph forms an invariant for algebraic isomorphisms as well

pullback and pushout constructions in c algebra theory abstract a systematic study of pullback and pushout diagrams is conducted in order to understand restricted direct sums and amalgamated free products of c algebras particular emphasis is given to the relations with tensor products both with the minimal and the maximal c tensor norm thus it is shown that pullback and pushout diagrams are stable under tensoring with a fixed algebra and stable under crossed products with a fixed group general tensor products between diagrams are also investigated the relations between the theory of extensions and pullback and pushout diagrams are explored in some detail the crowning result is that if three short exact sequences of c algebras are given with appropriate morphisms between the sequences allowing for pullback or pushout constructions at the levels of ideals algebras and quotients then the three new c algebras will again form a short exact sequence under some mild extra conditions as a generalization of a theorem of t a loring it is shown that each morphism between a pair of c algebras combined with its extension to the stabilized algebras gives rise to a pushout diagram this result has applications to corona extendibility and conditional projectivity finally the pullback and pushout constructions are applied to the class of noncommutative cw complexes defined by s eilers t a loring and g k pedersen j reine angew math 1998 499 101 143 to show that this category is stable under tensor products and under restricted direct sums

divisibility properties for c algebras we consider three notions of divisibility in the cuntz semigroup of a c algebra and show how they reflect properties of the c algebra we develop methods to construct simple and non simple c algebras with specific divisibility behaviour as a byproduct of our investigations we show that there exists a sequence an of simple unital infinite dimensional c algebras such that the product n 1an has a character

kms weights on graph c algebras abstract the paper contains a study of the gauge invariant kms weights for a generalized gauge action on a graph c algebra when the graph is irreducible and has the property that there are at most countably many roads to infinity in the graph a complete description is given of the structure of kms weights for the gauge action the structure is very rich and is identical with the structure of kms states for the restriction of the action to any corner defined by a projection in the fixed point algebra

crossed products by endomorphisms of c_0 x algebras abstract in the first part of the paper we develop a theory of crossed products of a c algebra a by an arbitrary not necessarily extendible endomorphism a a we consider relative crossed products c a j where j is an ideal in a and describe up to morita rieffel equivalence all gauge invariant ideals in c a j and give six term exact sequences determining their k theory we also obtain certain criteria implying that all ideals in c a j are gauge invariant and that c a j is purely infinite in the second part we consider a situation where a is a c 0 x algebra and is such that f a f a a a f c 0 x where is an endomorphism of c 0 x pictorially speaking is a mixture of a topological dynamical system x dual to c 0 x and a continuous field of homomorphisms x between the fibers a x x x of the corresponding c bundle for systems described above we establish efficient conditions for the uniqueness property gauge invariance of all ideals and pure infiniteness of c a j we apply these results to the case when x prim a is a hausdorff space in particular if the associated c bundle is trivial we obtain formulas for k groups of all ideals in c a j in this way we constitute a large class of crossed products whose ideal structure and k theory is completely described in terms of x x x x y where y is a closed subset of x

towards a theory of classification abstract the well known difficulties arising in a classification which is not set theoretically trivial involving what is sometimes called a non smooth quotient have been overcome in a striking way in the theory of operator algebras by the use of what might be called a classification functor the very existence of which is already a surprise here the notion of such a functor is developed abstractly and a number of examples are considered including those which have arisen for various classes of operator algebras

reducing stochasticity in the north atlantic oscillation index with coupled langevin equations we present a critical investigation of the functional relationship between the two pressure time series routinely used to define the index characterizing the north atlantic oscillation nao well known to regulate global climate variability and change first by a standard markov analysis we show that the standard nao index based on the pressure difference is not optimal in the sense of producing sufficiently reliable forecasts because it contains a dominating stochastic term in the corresponding langevin equation then we introduce a variationally optimized markov analysis involving two coupled langevin equations tailored to produce a nao quasi index having the desired minimum possible stochasticity the variationally optimized markov analysis is very general and can be applied in other physical situations involving two or more time series

identifying af algebras that are graph c algebras abstract we consider the problem of identifying exactly which af algebras are isomorphic to a graph c algebra we prove that any separable unital type i c algebra with finitely many ideals is isomorphic to a graph c algebra this result allows us to prove that a unital af algebra is isomorphic to a graph c algebra if and only if it is a type i c algebra with finitely many ideals we also consider nonunital af algebras that have a largest ideal with the property that the quotient by this ideal is the only unital quotient of the af algebra we show that such an af algebra is isomorphic to a graph c algebra if and only if its unital quotient is type i which occurs if and only if its unital quotient is isomorphic to m k for some natural number k all of these results provide vast supporting evidence for the conjecture that an af algebra is isomorphic to a graph c algebra if and only if each unital quotient of the af algebra is type i with finitely many ideals and bear relevance for the extension problem for graph c algebras

morphisms of extensions of c algebras pushing forward the busby invariant abstract we study completions of diagrams of extensions of c algebras in which all three c algebras in one of the rows and either the ideal or the quotient in the other are given along with the three morphisms between them we find universal solutions to all four of these problems under restrictions of varying severity on the given vertical maps and describe the solutions in terms of push outs and pull backs of certain diagrams our characterization of the universal solution to one of the diagrams yields a concrete description of various amalgamated free products this leads to new results about the k theory of amalgamated free products verifying the cuntz conjecture in certain cases we also obtain new results about extensions of matricial field c algebras verifying partially a conjecture of blackadar and kirchberg finally we show that almost commuting unitary matrices can be uniformly approximated by commuting unitaries when an index obstruction vanishes

extensions of cuntz krieger algebras abstract we show that a c algebra looking like a cuntz krieger algebra is a cuntz krieger algebra this implies that in an appropriate sense the class of cuntz krieger algebras is closed under extensions of real rank zero

graphs groupoids and cuntz krieger algebras we associate to each locally finite directed graphgtwo locally compact groupoidsgandg the unit space ofgis the space of one sided infinite paths ing andg is the reduction ofgto the space of paths emanating from a distinguished vertex we show that under certain conditions theirc algebras are morita equivalent the groupoidc algebrac g is the cuntz krieger algebra of an infinite 0 1 matrix defined byg and that the algebrasc g contain thec algebras used by doplicher and roberts in their duality theory for compact groups we then analyse the ideal structure of these groupoidc algebras using the general theory of renault and calculate theirk theory

the connes higson construction is an isomorphism let a be a separable c algebra and b a stable c algebra containing a strictly positive element we show that the group ext 1 2 sa b of unitary equivalence classes of extensions of sa by b modulo the extensions which are asymptotically split coincides with the group of homotopy classes of such extensions this is done by proving that the connes higson construction gives rise to an isomorphism between ext 1 2 sa b and the e theory group e a b of homotopy classes of asymptotic homomorphisms from s2a to b

poset block equivalence of integral matrices given square matrices b and b with a poset indexed block structure for which an ij block is zero unless i j when are there invertible matrices u and v with this required zero block structure such that ubv b we give complete invariants for the existence of such an equivalence for matrices over a principal ideal domain r as one application when r is a field we classify such matrices up to similarity by matrices respecting the block structure we also give complete invariants for equivalence under the additional requirement that the diagonal blocks of u and v have determinant 1 the invariants involve an associated diagram the k web of r module homomorphisms the study is motivated by applications to symbolic dynamics and c algebras

non simple purely infinite c algebras the hausdorff case abstract local and global definitions of pure infiniteness for a c algebra a are compared and equivalence between them is obtained if the primitive ideal space of a is hausdorff and of finite dimension if a has real rank zero or if a is approximately divisible sufficient criteria are given for local pure infiniteness of tensor products they yield that exact simple tensorially non prime c algebras are purely infinite if they have no semi finite lower semi continuous trace one obtains that a is isomorphic to a o if a is 1 purely infinite separable stable nuclear and prim a is a hausdorff space not necessarily of finite dimension

ordered k groups associated to substitutional dynamics the matsumoto k0 group is an interesting invariant of flow equivalence for symbolic dynamical systems because of its origin as the k theory of a certain c algebra which is also a flow invariant this group comes equipped with a flow invariant order structure we emphasize this order structure and demonstrate how methods from operator algebra and symbolic dynamics combine to allow a computation of it in certain cases including sturmian and primitive substitutional shifts in the latter case we show by example that the ordered group is a strictly finer invariant than the group itself

the ext class of an approximately inner automorphism let a be a simple unital at algebra of real rank zero it is shown below that the range of the natural map from the approximately inner automorphism group to kk a a coincides with the kernel of the map kk a a l 1 0 hom ki a ki a 1 introduction and preliminaries 1 1 an automorphism of a unital c algebra a is said to be an approximately inner automorphism if there is a sequence of unitaries un 2 a such that a limadun a for all a 2 a it follows that the induced map on k a is the identity map there is however an invariant of k theoretical interest which can occur nontrivial extensions may arise in the six term periodic sequence for the k theory of the mapping torus we show below that every extension does arise if a is a simple unital at algebra of real rank zero as an immediate corollary we obtain a stronger form of elliott s classification theorem for such algebras an invertible kk element that preserves positivity and the class of the unit lifts to an isomorphism 1 2 recall that a unital c algebra a is said to be a unital at algebra if it is expressible as the inductive limit of finite direct sums of algebras of the form mn c t with unital embeddings let a be a unital at algebra and let be an approximately inner automorphism of a the mapping torus of is the c algebra

continuous fields of kirchberg c algebras abstract in this paper we study the c algebras associated to continuous fields over locally compact metrizable zero dimensional spaces whose fibers are kirchberg c algebras satisfying the uct we show that these algebras are inductive limits of finite direct sums of kirchberg algebras and they are classified up to isomorphism by topological invariants

infinite non simple c algebras absorbing the cuntz algebra o abstract the first named author has given a classification of all separable nuclear c algebras a that absorb the cuntz algebra o we say that a absorbs o if a is isomorphic to a o motivated by this classification we investigate here if one can give an intrinsic characterization of c algebras that absorb o this investigation leads us to three different notions of pure infiniteness of a c algebra all given in terms of local algebraic conditions on the c algebra the strongest of the three properties strongly purely infinite is shown to be equivalent to absorbing o for separable nuclear c algebras that either are stable or have an approximate unit consisting of projections in a previous paper 2000 amer j math 122 637 666 we studied an intermediate and perhaps more natural condition purely infinite that extends a well known property for simple c algebras the weakest condition of the three weakly purely infinite is shown to be equivalent to the absence of quasitraces in an ultrapower of the c algebra the three conditions may be equivalent for all c algebras and we prove this to be the case for c algebras that are either simple of real rank zero or approximately divisible

k theoretic duality for shifts of finite type we will study the stable and unstable ruelle algebras associated to a hyperbolic homeomorphism of a compact space to do this we will describe a notion of k theoretic duality for algebras which generalizes spanier whitehead duality in topology a criterion for checking that it holds is presented as an application it is shown that the ruelle algebras which are associated to subshifts of finite type and agree with cuntz krieger algebras in this case satisfy this criterion and hence are dual

unbiased estimation of langevin dynamics from time series with application to hippocampal field potentials in vitro the last decade showed an increased interest in langevin equations for modeling time series recorded from complex dynamical systems these equations allow to discriminate between deterministic drift and stochastic diffusion components of the recorded time series in practice the estimation of drift and diffusion is often based on approximations of the models dynamics that are valid only for high sampling frequencies also model assessment is not or only indirectly performed potentially leading to false claims in this study we compare the performance of an asymptotically unbiased estimation method with a generally used approximate method demonstrating the necessity of using asymptotically unbiased estimators furthermore we describe how confidence intervals for the unknown parameters can be constructed and how model assessment can be carried out we apply the methodology to local field potentials recorded in vitro from mouse hippocampus from eight genetically different strains the recorded field potentials turn out to be well described by linearly damped langevin equations with parabolic diffusion the modeling enables a dynamical interpretation of the spectral power of the field potentials it reveals that observed spectral power differences in the field potentials across hippocampal regions are associated with differences in the deterministic component of the system and it reveals transiently active current dipoles which are not detectable by conventional methods also all estimated parameters have significant heritabilities which suggests that the langevin equations capture biological relevant aspects of electrical hippocampal activity

arbitrary order corrections for finite time drift and diffusion coefficients we address a standard class of diffusion processes with linear drift and quadratic diffusion coefficients these contributions to dynamic equations can be directly drawn from data time series however real data are constrained to finite sampling rates and therefore it is crucial to establish a suitable mathematical description of the required finite time corrections based on ito taylor expansions we present the exact corrections to the finite time drift and diffusion coefficients these results allow to reconstruct the real hidden coefficients from the empirical estimates we also derive higher order finite time expressions for the third and fourth conditional moments that furnish extra theoretical checks for this class of diffusion models the analytical predictions are compared with the numerical outcomes of representative artificial time series

classification of unital extensions of at algebras abstract we prove that the six term exact sequence in k theory together with the elliott invariants of the ideal and quotient is a complete invariant for certain unital extensions of a t algebras up to stable isomorphism we also give some necessary and sufficient conditions for such extensions being a t algebras or quasidiagonal extensions and prove the above invariant with the equivalence class of unit is a complete invariant for unital quasidiagonal extensions of a t algebras up to isomorphism

invariance of the cuntz splice we show that the cuntz splice induces stably isomorphic graph c algebras this result is a key step towards the recent complete classification of unital graph c algebras both with respect to k theoretical classification and with respect to geometrical classification in terms of an equivalence relation on the underlying graphs

corrigendum to classifying c algebras with both finite and infinite subquotients j funct anal 265 2013 449 468 abstract as recently pointed out by gabe a fundamental paper by elliott and kucerovsky concerning the absorption theory for c algebras contains an error and as a consequence we must report that lemma 4 5 in 3 is not true as stated in this corrigendum we prove an adjusted statement and explain why the error has no consequences to the main results of 3 in particular it is noted that all the authors claims concerning morita equivalence or stable isomorphism of graph c algebras remain correct as stated

c algebras of real rank zero abstract the concept of real rank of a c algebra is introduced as a non commutative analogue of dimension it is shown that real rank zero is equivalent to the previously defined conditions fs and hp and that it is invariant under strong morita equivalence in particular under stable isomorphism real rank zero is also invariant under inductive limits and split extensions and the class may well be regarded as the conceptual completion of the af algebras in some cases notably when the algebra is matroid it is shown that the multiplier algebra also has real rank zero although that is not true in general by a result of g j murphy this implies a weyl von neumann type result for self adjoint multiplier elements in these cases

classifying c algebras with both finite and infinite subquotients abstract we give a classification result for a certain class of c algebras a over a finite topological space x in which there exists an open set u of x such that u separates the finite and infinite subquotients of a we apply our results to c algebras arising from graphs

the blackadar handelman theorem for non unital c algebras abstract a well known theorem of blackadar and handelman states that every unital stably finite c algebra has a bounded quasitrace rather strong generalizations of stable finiteness to the non unital case can be obtained by either requiring the multiplier algebra to be stably finite or alternatively requiring it to be at least stably not properly infinite this paper deals with the question whether the blackadar handelman result can be extended to the non unital case with respect to these generalizations of stable finiteness two examples of c algebras are constructed the first one is a non unital stably commutative c algebra a that contradicts the weakest possible generalization of the blackadar handelman theorem the multiplier algebra of a is stably finite while a has no bounded quasitrace the second example is a simple c algebra b with no bounded quasitrace such that the multiplier algebras of all matrix algebras over b are not properly infinite

classification of certain infinite simple c algebras the class of c algebras that arise as the crossed product of a stable simple af algebra with a z action determined by an automorphism which maps a projection in the algebra onto a proper subprojection is proved to consist of simple purely infinite c algebras and a specific subclass of it is proved to be classified by k theory this subclass is large enough to exhaust all possible k groups if g0 and g1 are countable abelian groups with g1 torsion free as it must be then there is a c algebras a in the classified subclass with k0 a g0 and k 1 a g1 the subclass contains the cuntz algebras o with n even and the cuntz krieger algebras o a with k0 o a of finite old order and it is closed under forming inductive limits the c algebras in the classified subclass can be viewed as classifiable models in a strong sense of general simple purely infinite c algebras with the same k theory

graph algebras exel laca algebras and ultragraph algebras coincide up to morita equivalence we prove that the classes of graph algebras exel laca algebras and ultra graph algebras coincide up to morita equivalence this result answers the long standing open question of whether every exel laca algebra is morita equivalent to a graph algebra given an ultragraph g we construct a directed graph e such that c g is isomorphic to a full corner of c e as applications we characterize real rank zero for ultragraph algebras and describe quotients of ultragraph algebras by gauge invariant ideals

e theory for c algebras over topological spaces abstract we define e theory for separable c algebras over second countable topological spaces and establish its basic properties this includes an approximation theorem that relates the e theory over a general space to the e theories over finite approximations to this space we obtain effective criteria for determining the invertibility of e theory elements over possibly infinite dimensional spaces furthermore we prove a universal multicoefficient theorem for c algebras over totally disconnected metrisable compact spaces

von neumann algebras of strongly connected higher rank graphs we investigate the factor types of the extremal kms states for the preferred dynamics on the toeplitz algebra and the cuntz krieger algebra of a strongly connected finite k graph for inverse temperatures above 1 all of the extremal kms states are of type mathrm i infty at inverse temperature 1 there is a dichotomy if the k graph is a simple k dimensional cycle we obtain a finite type mathrm i factor otherwise we obtain a type iii factor whose connes invariant we compute in terms of the spectral radii of the coordinate matrices and the degrees of cycles in the graph

stability of a σp unital continuous field algebra we study the question of whether stability is preserved under the operation of forming a continuous field algebra this is not necessarily true when the base space is infinite dimensional however it is always true when the base space is an n cube or an n torus and when the continuous field algebra is p unital specifically we prove the following theorem 0 1 let a be a p unital separable maximal full algebra of operator fields with base space either an n cube x 0 1 n or an n torus x tn and fibre algebras ax x x if ax is stable for all x x then a is a stable c algebra we also show that under the same hypotheses the corona factorization property is also preserved under the formation of continuous field algebras theorem 0 2 let a be a p unital separable maximal full algebra of operator fields with base space either an n cube x 0 1 n or an n torus x tn and fibre algebras ax x x if ax has the corona factorization property for all x x then a also has the corona factorization property

lifting kk elements asymptotic unitary equivalence and classification of simple c algebras let a and c be two unital simple c algebras with tracial rank zero suppose that c is amenable and satisfies the universal coefficient theorem denote by kke c a the set of those in kk c a for which k0 c 0 k0 a 0 and 1c 1a suppose that kke c a we show that there is a unital monomorphism c a such that suppose that c is a unital ah algebra and is a continuous affine map for which t p t p for all projections p in all matrix algebras of c and any tt a where t a is the simplex of tracial states of a and is the convex set of faithful tracial states of c we prove that there is a unital monomorphism c a such that induces both and suppose that h c a is a unital monomorphism and hom k1 c aff a we show that there exists a unital monomorphism c a such that h in kk c a t t h for all tracial states t and the associated rotation map can be given by denote by kkt c a the set of compatible pairs where kle c a and is a continuous affine map from t a to together with a result on asymptotic unitary equivalence in h lin asymptotic unitary equivalence and asymptotically inner automorphisms arxiv math 0703610 2007 this provides a bijection from the asymptotic unitary equivalence classes of unital monomorphisms from c to a to where is a subgroup related to vanishing rotation maps as an application combining these results with a result of w winter w winter localizing the elliott conjecture at strongly self absorbing c algebras arxiv 0708 0283v3 2007 we show that two unital amenable simple stable c algebras are isomorphic if they have the same elliott invariant and the tensor products of these c algebras with any uhf algebra have tracial rank zero in particular if a and b are two unital separable simple stable c algebras with unique tracial states which are inductive limits of c algebras of type i then they are isomorphic if and only if they have isomorphic elliott invariants

the distribution based p value for the outlier sum in differential gene expression analysis outlier sums were proposed by tibshirani hastie 2007 and wu 2007 for detecting outlier genes where only a small subset of disease samples shows unusually high gene expression but they did not develop their distributional properties and formal statistical inference in this study a new outlier sum for detection of outlier genes is proposed its asymptotic distribution theory is developed and the p value based on this outlier sum is formulated its analytic form is derived on the basis of the large sample theory we compare the proposed method with existing outlier sum methods by power comparisons our method is applied to dna microarray data from samples of primary breast tumors examined by huang et al 2003 the results show that the proposed method is more efficient in detecting outlier genes

mathcal c _ 0 x algebras stability and strongly self absorbing mathcal c algebras we study permanence properties of the classes of stable and so called mathcal d stable mathcal c algebras respectively more precisely we show that a mathcal c 0 x algebra a is stable if all its fibres are provided that the underlying compact metrizable space x has finite covering dimension or that the cuntz semigroup of a is almost unperforated a condition which is automatically satisfied for mathcal c algebras absorbing the jiang su algebra mathcal z tensorially furthermore we prove that if mathcal d is a k 1 injective strongly self absorbing mathcal c algebra then a absorbs mathcal d tensorially if and only if all its fibres do again provided that x is finite dimensional this latter statement generalizes results of blanchard and kirchberg we also show that the condition on the dimension of x cannot be dropped along the way we obtain a useful characterization of when a mathcal c algebra with weakly unperforated cuntz semigroup is stable which allows us to show that stability passes to extensions of mathcal z absorbing mathcal c algebras

rokhlin dimension for flows we introduce a notion of rokhlin dimension for one parameter automorphism groups of c algebras this generalizes kishimoto s rokhlin property for flows and is analogous to the notion of rokhlin dimension for actions of the integers and other discrete groups introduced by the authors and zacharias in previous papers we show that finite nuclear dimension and absorption of a strongly self absorbing c algebra are preserved under forming crossed products by flows with finite rokhlin dimension and that these crossed products are stable furthermore we show that a flow on a commutative c algebra arising from a free topological flow has finite rokhlin dimension whenever the spectrum is a locally compact metrizable space with finite covering dimension for flows that are both free and minimal this has strong consequences for the associated crossed product c algebras those containing a non zero projection are classified by the elliott invariant for compact manifolds this consists of topological k theory together with the space of invariant probability measures and a natural pairing given by the ruelle sullivan map

universal coefficient theorems for the stable ext groups let a be a unital separable nuclear c algebra and let b be a stable c algebra using k theory and kk theory we establish universal coefficient theorems for the stable ext groups of unital extensions of a by b when a and b have certain properties which generalize a result of l brown and m dadarlat for the strong ext groups the class of extensions being studied are also enlarged

the k theoretical range of cuntz krieger algebras abstract we augment restorff s classification of purely infinite cuntz krieger algebras by describing the range of his invariant on purely infinite cuntz krieger algebras we also describe its range on purely infinite graph c algebras with finitely many ideals and provide unital range results for purely infinite cuntz krieger algebras and unital purely infinite graph c algebras

classification of extensions of classifiable c algebras abstract for a certain class of extensions e 0 b e a 0 of c algebras in which b and a belong to classifiable classes of c algebras we show that the functor which sends e to its associated six term exact sequence in k theory and the positive cones of k 0 b and k 0 a is a classification functor we give two independent applications addressing the classification of a class of c algebras arising from substitutional shift spaces on one hand and of graph algebras on the other the former application leads to the answer of a question of carlsen and the first named author concerning the completeness of stabilized matsumoto algebras as an invariant of flow equivalence the latter leads to the first classification result for nonsimple graph c algebras

an algebraic approach to the radius of comparison the radius of comparison is an invariant for unital c algebras which extends the theory of covering dimension to noncommutative spaces we extend its definition to general c algebras and give an algebraic as opposed to functional theoretic reformulation this yields new permanence properties for the radius of comparison which strengthen its analogy with covering dimension for commutative spaces we then give several applications of these results new examples of c algebras with finite radius of comparison are given and the question of when the cuntz classes of finitely generated hilbert modules form a hereditary subset of the cuntz semigroup is addressed most interestingly perhaps we treat the question of when a full hereditary subalgebra b of a stable c algebra a is itself stable giving a characterization in terms of the radius of comparison we also use the radius of comparison to quantify the least n for which a c algebra d without bounded 2 quasitraces or unital quotients has the property that mn d is stable

extensions for af algebras and dimension groups let a c be approximately finite dimensional af c algebras with a nonunital and c unital suppose that either i a is the algebra of compact operators or ii both a c are simple the classification of extensions of a by c is studied here by means of elliott s dimension groups in case i the weak ext group of c is shown to be extz ko c z and the strong ext group is an extension of a cyclic group by the weak ext group conditions under which either ext group is trivial are determined in case ii there is an unnatural and complicated group structure on the classes of extensions when a has only finitely many pure finite traces and somewhat more generally our motivating theme is to consider extensions of c algebras by other than the algebra of compact operators because af algebras are describable in terms of partially ordered groups they seem particularly suitable for this extension theory as the ordered groups arising from simple af algebras are fairly well understood it turns out that one can solve completely the problem of classifying simple by simple af algebras when the finite trace space of the bottom af algebra has finite dimensional dual in the course of doing this we establish formulae for the usual strong and weak ext groups of af algebras our homological approach to this differs from the computational viewpoint of pimsner and popa 14 15 we consider short exact sequences extensions of c algebras a b c with b an af algebra there is a translation to extensions within a class of partially ordered abelian groups and distinguished subset known as dimension groups with interval via the functor ko0 this translation is reversible owing to a recent result of l brown that an extension of an af algebra by an af algebra is af so all c extensions are represented as dimension group extensions with the appropriate notion of equivalence extending strong equivalence as defined in 3 p 268 when a is the algebra of compact operators on a separable hilbert space the equivalence classes admit a limited additive operation often forming a disjoint union of groups a single group results if for example both a and c are simple with a unitless but not necessarily stable 1 deals with the appropriate definitions of extensions dimension groups equivalence and the translation between af algebras and dimension groups much of this is well known in the second section it is shown that if a is simple stable and c is received by the editors december 11 1979 and in revised form march 25 1981 1980 mathematics subject classification primary 46l35 secondary 54a22 16a54 16a56 06f20 supported in part by an operating grant from nserc of canada d1982 american mathematical society 0002 9947 82 0000 1 059 09 75

a class of c algebras generalizing both graph algebras and homeomorphism c algebras i fundamental results we introduce a new class of c algebras which is a generalization of both graph algebras and homeomorphism c algebras this class is very large and also very tractable we prove the so called gauge invariant unique ness theorem and the cuntz krieger uniqueness theorem and compute the k groups of our algebras

the corona factorization property and refinement monoids the corona factorization property of a c algebra originally defined to study extensions of c algebras has turned out to say something important about intrinsic struc tural properties of the c algebra we show in this paper that a unital c algebra a of real rank zero has the corona factorization property if and only if its monoid v a of murray von neumann equivalence classes of projections in matrix algebras over a has a certain rather weak comparability property that we call the corona factorization property for monoids we show that a projection in such a c algebra is properly infinite if and only if a multiple of it is properly infinite the latter result is obtained from some more general result we establish about conical refinement monoids we show that the set of order units together with the zero element in a conical refinement monoid is again a refinement monoid under the assumption that the monoid satisfies weak divisibility and if u is an element in a refinement monoid such that nu is properly infinite then u can be written as a sum u s t such that ns and nt are properly infinite

a class of c algebras generalizing both graph algebras and homeomorphism c algebras iv pure infiniteness this is the final one in the series of papers where we introduce and study the c algebras associated with topological graphs in this paper we get a sufficient condition on topological graphs so that the associated c algebras are simple and purely infinite using this result we give one method to construct all kirchberg algebras as c algebras associated with topological graphs

large fredholm triples abstract we give several equivalent condition for busby extensions of a given algebra to be absorbing considerably improving our earlier results g a elliott d kucerovsky an abstract brown douglas fillmore absorption theorem pacific j math 198 2001 385 409 and establish sufficient conditions for fredholm triples to be absorbing in a suitable sense as an application of one of our criteria we prove a multivariable brown douglas fillmore type theorem

leavitt r algebras over countable graphs embed into l2 r abstract for a commutative ring r with unit we show that the leavitt path algebra l r e of a graph e embeds into l 2 r precisely when e is countable before proving this result we prove a generalised cuntz krieger uniqueness theorem for leavitt path algebras over r

adaptive trimmed t statistics for identifying predominantly high expression in a microarray experiment often interesting candidate tumor markers are not only genes that show homogeneously higher expression hhe in tumor samples compared to control samples but also genes with only predominantly higher expression phe i e genes which exhibit higher expression in at least 80 per cent of tumor samples standard parametric test statistics used in the analysis of microarray experiments may fail with phe as a consequence of the mixture of distributions present in the tumor group as alternative we consider trimmed t statistics which compare group mean values after removing outliers in each group the trimming proportion can be chosen adaptively either based on a boxplot outlier detection rule or by optimization over a series of tests with varying trimming proportions the trimmed t statistics can be plugged into the significance analysis of microarrays sam procedure yielding the modified boxplot rule test modbox and the modified optimization test modopt respectively by means of simulation of microarray experiments we show that modopt is superior to contenders in detecting phe while there is only little loss in efficiency under hhe compared to sam analysis of a real microarray experiment revealed that out of nearly 29 000 genes about 417 genes exhibiting phe are detected by modopt but missed by sam

the suspension of a graph and associated c algebras abstract given a directed graph e we construct for each real number l a quiver whose vertex space is the topological realisation of e and whose edges are directed paths of length l in the vertex space these quivers are not topological graphs in the sense of katsura nor topological quivers in the sense of muhly and tomforde we prove that when l 1 and e is finite the infinite path space of the associated quiver is homeomorphic to the suspension of the one sided shift of e we call this quiver the suspension of e we associate both a toeplitz algebra and a cuntz krieger algebra to each of the quivers we have constructed and show that when l 1 the cuntz krieger algebra admits a natural faithful representation on the l 2 space of the suspension of the one sided shift of e for graphs e in which sufficiently many vertices both emit and receive at least two edges and for rational values of l we show that the toeplitz algebra and the cuntz krieger algebra of the associated quiver are homotopy equivalent to the toeplitz algebra and cuntz krieger algebra respectively of a graph that can be regarded as encoding the lth higher shift associated to the one sided shift space of e

non simple purely infinite c algebras a c algebra a is defined to be purely infiniteif there are no characters on a a nd if for every pair of positive elements a b in a such that b lies in the closed two sided ideal generated by a there exists a sequence rn in a such that rn arn b this definition agrees with the usual definition by j cuntz when a is simple it is shown that the property of being purely infinite is preserved under extensions morita equivalence inductive limits and it passes to quotients and to hereditary sub c algebras it is shown that a is purely infinite for every c algebra a purely infinite c algebras admit no traces and conversely an approximately divisible exact c algebra is purely infinite if it admits no nonzero trace

controlling the false discovery rate a practical and powerful approach to multiple testing summary the common approach to the multiplicity problem calls for controlling the familywise error rate fwer this approach though has faults and we point out a few a different approach to problems of multiple significance testing is presented it calls for controlling the expected proportion of falsely rejected hypotheses the false discovery rate this error rate is equivalent to the fwer when all hypotheses are true but is smaller otherwise therefore in problems where the control of the false discovery rate rather than that of the fwer is desired there is potential for a gain in power a simple sequential bonferronitype procedure is proved to control the false discovery rate for independent test statistics and a simulation study shows that the gain in power is substantial the use of the new procedure and the appropriateness of the criterion are illustrated with examples

decomposition rank and absorbing extensions of type i algebras abstract we prove the following let a and b be separable c algebras suppose that b is a type i c algebra such that i b has only infinite dimensional irreducible representations and ii b has finite decomposition rank if 0 b c a 0 is a unital homogeneous exact sequence with busby invariant then the extension is absorbing in the case of infinite decomposition rank we provide a counterexample specifically we construct a unital homogeneous split exact sequence of the form 0 c z k c c 0 which is not absorbing in this example z is an infinite dimensional compact second countable topological space this gives a counterexample to the natural infinite dimensional generalization of the result of pimsner popa and voiculescu

af labeled graph c algebras abstract it is known that a graph c algebra c e is approximately finite dimensional af if and only if the graph e has no loops in this paper we consider the question of when a labeled graph c algebra c e l b is af a notion of loop in a labeled space e l b is defined when b is the smallest one among the accommodating sets that are closed under relative complements and it is proved that if a labeled graph c algebra is af the labeled space has no loops a sufficient condition for a labeled space to give rise to an af algebra is also given for graph c algebras c e this sufficient condition is also a necessary one besides we discuss other equivalent conditions for a graph c algebra to be af in the setting of labeled graphs and prove that these conditions are not always equivalent by invoking various examples

on stability ofc algebras letabe a unitalc algebra i e aadmits a countable approximate unit it is proved thatais stable i e ais isomorphic toa k where k is the algebra of compact operators on a separable hilbert space if and only if for each positive elementa aand eache 0 there exists a positive elementb asuch that ab eandx x a xx bfor somexina using this characterization it is proved among other things that the inductive limit of any sequence of unital stablec algebras is stable and that the crossed product of a unital stablec algebra by a discrete group is again stable

homology for higher rank graphs and twisted c algebras abstract we introduce a homology theory for k graphs and explore its fundamental properties we establish connections with algebraic topology by showing that the homology of a k graph coincides with the homology of its topological realisation as described by kaliszewski et al we exhibit combinatorial versions of a number of standard topological constructions and show that they are compatible from a homological point of view with their topological counterparts we show how to twist the c algebra of a k graph by a t valued 2 cocycle and demonstrate that examples include all noncommutative tori in the appendices we construct a cubical set q from a k graph and demonstrate that the homology and topological realisation of coincide with those of q as defined by grandis

kms states on the c algebras of finite graphs abstract we consider a finite directed graph e and the gauge action on its toeplitz cuntz krieger algebra viewed as an action of r for inverse temperatures larger than a critical value c we give an explicit construction of all the kms states if the graph is strongly connected then there is a unique kms c state and this state factors through the quotient map onto c e our approach is direct and relatively elementary

a separable brown douglas fillmore theorem and weak stability we give a separable brown douglas fillmore theorem let a be a separable amenable c algebra which satisfies the approximate uct b be a unital separable amenable purely infinite simple c algebra and h 1 h 2 a b be two monomorphisms we show that h 1 and h 2 are approximately unitarily equivalent if and only if h 1 h 2 in kl a b we prove that for any e 0 and any finite subset f a there exist 0 and a finite subset g a satisfying the following for any amenable purely infinite simple c algebra b and for any contractive positive linear map l a b such that l ab l a l b 0 there is 0 such that in any unital amenable purely infinite simple c algebra b if uv e i vu for a pair of unitaries then there exists a pair of unitaries u 1 and v 1 in b such that u 1 v 1 e i v 1 u 1 u 1 u e and v 1 v e

extensions contained in ideals we prove a weyl von neumann type absorption theorem for extensions which are not full and give a condition for constructing infinite repeats contained in an ideal we also clear up some questions associated with the purely large criterion for full extensions to be absorbing

graph c algebras branching systems and the perron frobenius operator in this paper we show how to produce a large number of representations of a graph c algebra in the space of the bounded linear operators in l2 x these representations are very concrete and in the case of graphs that satisfy condition l we use our techniques to realize the associated graph c algebra as a subalgebra of the bounded operators in l2 r we also show how to describe the perron frobenius operator of ergodic theory in terms of the representations we associate to a graph

on the classification of nonsimple graph c algebras we prove that a graph c algebra with exactly one proper nontrivial ideal is classified up to stable isomorphism by its associated six term exact sequence in k theory we prove that a similar classification also holds for a graph c algebra with a largest proper ideal that is an af algebra our results are based on a general method developed by the first named author with restorff and ruiz as a key step in the argument we show how to produce stability for certain full hereditary subalgebras associated to such graph c algebras we further prove that except under trivial circumstances a unique proper nontrivial ideal in a graph c algebra is stable

realizations of af algebras as graph algebras exel laca algebras and ultragraph algebras abstract we give various necessary and sufficient conditions for an af algebra to be isomorphic to a graph c algebra an exel laca algebra and an ultragraph c algebra we also explore consequences of these results in particular we show that all stable af algebras are both graph c algebras and exel laca algebras and that all simple af algebras are either graph c algebras or exel laca algebras in addition we obtain a characterization of af algebras that are isomorphic to the c algebra of a row finite graph with no sinks