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

actions of symbolic dynamical systems on c algebras ii simplicity of c symbolic crossed products and some examples a c symbolic dynamical system mathcal a rho sigma consists of a unital c algebra mathcal a and a finite family rho alpha alpha in sigma of endomorphisms of mathcal a indexed by symbols of satisfying some conditions the endomorphisms rho alpha alpha in sigma yield both a subshift and a c algebra of a hilbert c bimodule the obtained c algebra is regarded as a crossed product of mathcal a by the subshift we will study simplicity condition of these c algebras some examples such as irrational rotation cuntz krieger algebras will be studied

representations of etale groupoids on l p spaces for p 1 we study representations of etale groupoids on l p spaces our main result is a generalization of renault s disintegration theorem for representations of etale groupoids on hilbert spaces we establish a correspondence between l p representations of an etale groupoid g contractive l p representations of c c g and tight regular l p representations of any countable inverse semigroup of open slices of g that is a basis for the topology of g we define analogs f p g and f red p g of the full and reduced groupoid c algebras using representations on l p spaces as a consequence of our main result we deduce that every contractive representation of f p g or f red p g is automatically completely contractive examples of our construction include the following natural families of banach algebras discrete group l p operator algebras the analogs of cuntz algebras on l p spaces and the analogs of af algebras on l p spaces our results yield new information about these objects their matricially normed structure is uniquely determined more generally groupoid l p operator algebras provide analogs of several families of classical c algebras such as cuntz krieger c algebras tiling c algebras and graph c algebras

duals of compact lie groups realized in the cuntz algebras and their actions on c algebras abstract as a first step towards a new duality theorem for compact groups we consider a representation category t g of a compact lie group g u d c whose objects are the tensor powers of the defining representation and whose arrows are the intertwiners we associate to t g in a natural way a c algebra og which can be identified with the fixed points of the cuntz algebra od under the natural action of g og carries a canonical endomorphism g and t g can be reconstructed from og g if g su d then og is simple we give conditions for an endomorphism of a unital c algebra a to determine an action of t su d on a such actions correspond to monomorphisms of osu d into a with natural intertwining properties

dynamical systems associated to separated graphs graph algebras and paradoxical decompositions abstract we attach to each finite bipartite separated graph e c a partial dynamical system e c f where e c is a zero dimensional metrizable compact space f is a finitely generated free group and is a continuous partial action of f on e c the full crossed product c algebra o e c c e c f is shown to be a canonical quotient of the graph c algebra c e c of the separated graph e c similarly we prove that for any field k the algebraic crossed product l k ab e c c k e c alg f is a canonical quotient of the leavitt path algebra l k e c of e c the monoid v l k ab e c of isomorphism classes of finitely generated projective modules over l k ab e c is explicitly computed in terms of monoids associated to a canonical sequence of separated graphs using this we are able to construct an action of a finitely generated free group f on a zero dimensional metrizable compact space z such that the type semigroup s z f k is not almost unperforated where k denotes the algebra of clopen subsets of z finally we obtain a characterization of the separated graphs e c such that the canonical partial action of f on e c is topologically free

exchange leavitt path algebras and stable rank abstract we characterize those leavitt path algebras which are exchange rings in terms of intrinsic properties of the graph and show that the values of the stable rank for these algebras are 1 2 or concrete criteria in terms of properties of the underlying graph are given for each case

semiprojectivity and properly infinite projections in graph c algebras abstract we give a complete description of which unital graph c algebras are semiprojective and use it to disprove two conjectures by blackadar to do so we perform a detailed analysis of which projections are properly infinite in such c algebras

kumjian pask algebras of finitely aligned higher rank graphs abstract we extend the definition of kumjian pask algebras to include algebras associated to finitely aligned higher rank graphs we show that these kumjian pask algebras are universally defined and have a graded uniqueness theorem we also prove the cuntz krieger uniqueness theorem to do this we use a groupoid approach as a consequence of the graded uniqueness theorem we show that every kumjian pask algebra is isomorphic to the steinberg algebra associated to its boundary path groupoid we then use steinberg algebra results to prove the cuntz krieger uniqueness theorem and also to characterize simplicity and basic simplicity

equilibrium and ground states from cayley graphs abstract we present a general framework for the study of kms states of generalized gauge actions on the c algebra of a cayley graph which is pointed by considering the neutral element of the group as a distinguished vertex we use this framework to give a concrete description of a particular kind of kms states on the c algebras that we call abelian kms states if the group is nilpotent all kms states are abelian and our analysis gives the full picture in this case we then describe the ground states that are limits of abelian kms states when the temperature goes to zero

graph c algebras with real rank zero given a row finite directed graph e a universal c algebra c e generated by a family of partial isometries and projections subject to the relations determined by e is associated to the graph e the cuntz krieger algebras are those graph c algebras associated to some finite graphs we prove that a graph c algebra c e has real rank zero in the sense that the set of invertible self adjoint elements is dense in the set of all self adjoint elements in c e or in the unitization of c e if c e is nonunital if and only if e satisfies a loop condition k that is analogous to the condition for a finite 0 1 matrix a under which cuntz analyzed the ideal structure of the cuntz krieger algebra oa

purely infinite partial crossed products let a g be a partial dynamical system we show that there is a bijective correspondence between g invariant ideals of a and ideals in the partial crossed product a rg provided the action is exact and residually topologically free assuming in addition a technical condition automatic when a is abelian we show that a rg is purely infinite if and only if the positive nonzero elements in a are properly infinite in a rg as an application we verify pure infiniteness of various partial crossed products including realisations of the cuntz algebras on oa on and oz as partial crossed products

a going down principle for ample groupoids and the baum connes conjecture abstract we study a going down or restriction principle for ample groupoids and its applications the going down principle for locally compact groups was developed by chabert echterhoff and oyono oyono and allows to study certain functors that arise in the context of the topological k theory of a locally compact group in terms of their restrictions to compact subgroups we extend this principle to the class of ample hausdorff groupoids using le gall s groupoid equivariant version of kasparov s bivariant kk theory moreover we provide an application to the baum connes conjecture for ample groupoids which are strongly amenable at infinity this result in turn is then used to relate the baum connes conjecture for an ample groupoid group bundle which is strongly amenable at infinity to the baum connes conjecture for the fibres

the nuclear dimension of graph c algebras abstract consider a graph c algebra c e with a purely infinite ideal i possibly all of c e such that i has only finitely many ideals and c e i is approximately finite dimensional we prove that the nuclear dimension of c e is 1 if i has infinitely many ideals then the nuclear dimension of c e is either 1 or 2

cartan subalgebras in c algebras existence and uniqueness we initiate the study of cartan subalgebras in c algebras with a particular focus on existence and uniqueness questions for homogeneous c algebras these questions can be analyzed systematically using the theory of fiber bundles for group c algebras while we are able to find cartan subalgebras in c algebras of many connected lie groups there are classes of discrete groups for instance non abelian free groups whose reduced group c algebras do not have any cartan subalgebras moreover we show that uniqueness of cartan subalgebras usually fails for classifiable c algebras however distinguished cartan subalgebras exist in some cases for instance in nuclear uniform roe algebras

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

c algebras associated to boolean dynamical systems copyright 2017 elsevier b v or its licensors or contributors this is the authors accepted and refereed manuscript to the article

pseudogroups and their etale groupoids abstract a pseudogroup is a complete infinitely distributive inverse monoid such inverse monoids bear the same relationship to classical pseudogroups of transformations as frames do to topological spaces the goal of this paper is to develop the theory of pseudogroups motivated by applications to group theory c algebras and aperiodic tilings our starting point is an adjunction between a category of pseudogroups and a category of etale groupoids from which we are able to set up a duality between spatial pseudogroups and sober etale groupoids as a corollary to this duality we deduce a non commutative version of stone duality involving what we call boolean inverse semigroups and boolean etale groupoids as well as a generalization of this duality to distributive inverse semigroups non commutative stone duality has important applications in the theory of c algebras it is the basis for the construction of cuntz and cuntz krieger algebras and in the case of the cuntz algebras it can also be used to construct the thompson groups we then define coverages on inverse semigroups and the resulting presentations of pseudogroups as applications we show that paterson s universal groupoid is an example of a booleanization and reconcile exel s recent work on the theory of tight maps with the work of the second author

when is the cuntz krieger algebra of a higher rank graph approximately finite dimensional evans d g and sims a when is the cuntz krieger algebra of a higher rank graph approximately finite dimensional preprint arxiv 1112 4549v1

cartan subalgebras for non principal twisted groupoid c algebras abstract renault proved in 2008 22 theorem 5 2 that if g is a topologically principal groupoid then c 0 g 0 is a cartan subalgebra in c r g for any twist over g however there are many groupoids which are not topologically principal yet their twisted c algebras admit cartan subalgebras this paper gives a dynamical description of a class of such cartan subalgebras by identifying conditions on a 2 cocycle c on g and a subgroupoid s g under which c r s c is cartan in c r g c when g is a discrete group we also describe the weyl groupoid and twist associated to these cartan pairs under mild additional hypotheses

the noncommutative geometry of graph c algebras i the index theorem we investigate conditions on a graph c algebra for the existence of a faithful semifinite trace using such a trace and the natural gauge action of the circle on the graph algebra we construct a smooth 1 summable semi finite spectral triple the local index theorem allows us to compute the pairing with k theory this produces invariants in the k theory of the fixed point algebra and these are invariants for a finer structure than the isomorphism class of c e

labelled space c algebras as partial crossed products and a simplicity characterization abstract a partial action is associated with a normal weakly left resolving labelled space such that the crossed product and labelled space c algebras are isomorphic an improved characterization of simplicity for labelled space c algebras is given and applied to c algebras of subshifts

a borsuk ulam theorem for orthogonal tk and zpr actions and applications abstract a version if the borsuk ulam theorem is proved for the torus tk and p torus zpr we deal with the case of a nonempty fixed point set of groups on the sphere of representation as an application a geometrical index theory is introduced for these groups the index is used to obtain the existence of multiple critical points for functions invariant under tk or zpr action

noncommutative manifolds from graph and k graph c algebras in pren we constructed smooth 1 summable semifinite spectral triples for graph algebras with a faithful trace and in prs we constructed k summable semifinite spectral triples for k graph algebras in this paper we identify classes of graphs and k graphs which satisfy a version of connes conditions for noncommutative manifolds

endomorphisms of c algebras cross products and duality for compact groups on definit une nouvelle sorte de produit croise d une c algebre par des semigroupes d endomorphismes avec des proprietes reliees a la symetrie de permutation et a l existence de conjugues un groupe compact est alors defini intrinsequement par son action duale sur le produit croise cette construction donne une caracterisation des duaux de groupes compacts abstraits qui est hors d atteinte de la theorie de dualite de taunaka kein et est independante de cette theorie ceci resout le probleme de demontrer l existence d un groupe de jauge global compact en physique des particules etant seulement donnees les observables locales

compact differentiable transformation groups on exotic spheres 0 introduction 355 1 statement of the main results 357 2 higher dimensional subgroups of o n 1 358 3 higher dimensional transformation groups on homology spheres geometric weight systems and orbit structures 360 4 higher dimensional transformation groups on homotopy spheres and the proof of theorem b 375 5 degree of symmetry of exotic spheres revisited 381 6 large transformation groups on exotic spheres in bp 1 384

kms weights on groupoid and graph c algebras abstract the paper contains a description of the kms weights for the one parameter action on the reduced c algebra of a second countable locally compact hausdorff etale groupoid arising from a continuous real valued homomorphism satisfying two conditions the result is subsequently applied to identify the kms weights for the gauge action on a simple graph algebra the von neumann algebra generated by the gns representation of an extremal kms weight is a factor and tools are developed to determine its type the paper concludes with three examples to illustrate the results

on the orbit structures ofsu n actions on manifolds of the type of euclidean spherical or projective spaces on etudie les structures d orbites des actions su n sur des espaces test qui sont du type cohomologique des espaces euclidiens spheriques ou projectifs

semigroupoid c algebras abstract a semigroupoid is a set equipped with a partially defined associative operation given a semigroupoid we construct a c algebra o from it we then present two main examples of semigroupoids namely the markov semigroupoid associated to an infinite 0 1 matrix and the semigroupoid associated to a row finite higher rank graph without sources in both cases the semigroupoid c algebra is shown to be isomorphic to the algebras usually attached to the corresponding combinatorial object namely the cuntz krieger algebras and the higher rank graph c algebras respectively in the case of a higher rank graph d it follows that the dimension function d is superfluous for defining the corresponding c algebra

the brauer group of a locally compact groupoid we define the brauer group br g of a locally compact groupoid g to be the set of morita equivalence classes of pairs a consisting of an elementary c bundle a over g 0 satisfying fell s condition and an action of g on a by isomorphisms when g is the transformation groupoid x h then br g is the equivariant brauer group br h x in addition to proving that br g is a group we prove three isomorphism results first we show that if g and h are equivalent groupoids then br g and br h are isomorphic this generalizes the result that if g and h are groups acting freely and properly on a space x say g on the left and h on the right then br g x h and br h g x are isomorphic secondly we show that the subgroup br0 g of br g consisting of classes a with a having trivial dixmier douady invariant is isomorphic to a quotient e g of the collection tw g of twists over g finally we prove that br g is isomorphic to the inductive limit ext g inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i of the groups e g x where x varies over all principal g spaces x and g x is the imprimitivity groupoid associated to x

homoclinic solutions of hamiltonian systems with symmetry abstract we prove the existence of infinitely many homoclinic solutions for a first order hamiltonian system symmetric with respect to an action of a compact lie group by means of variational methods we make no convexity assumption on the hamiltonian

graph inverse semigroups their characterization and completion abstract graph inverse semigroups generalize the polycyclic inverse monoids and play an important role in the theory of c algebras in this paper we characterize such semigroups and show how they may be completed under suitable conditions to form what we call the cuntz krieger semigroup of the graph this semigroup is proved to be the ample semigroup of a topological groupoid associated with the graph and the semigroup analogue of the leavitt path algebra of the graph

phase transition in the car algebra abstract the paper develops a method to construct one parameter groups of automorphisms on a uhf algebra with a prescribed field of kms states

congruences on graph inverse semigroups abstract graph inverse semigroups were defined by ash and hall in 1975 they found necessary and sufficient conditions for the semigroups to be congruence free in this paper we give a classification of congruences on a graph inverse semigroup in terms of the underlying graph as a consequence we show that the inverse graph semigroup of a finite graph is congruence noetherian

the topological version of groups generated by reflections that is g h is a coxeter system 6 11 the study of groups generated by differentiable reflections was initiated by weyl 15 and koszul 10 and they proved that if the manifold is simply connected then g is a coxeter transformation group then came the fixed point results of the hsiang brothers saying essentially that the geometric behavior of groups generated by differentiable reflections on acyclic spaces or spheres is homologically similar to ordinary groups of reflections bredon 4 pointed out some errors and gaps in the proofs in 9 and proved himself some weaker versions of the results but the authors of 9 later constructed new correct proofs still 4 contains a new useful contribution to the general theory namely the sheaf theoretic approach of lemma 3 1 in 4 or lemma 4 in 8 ore proposition 2 2 is based upon this

finite simple labeled graph c algebras of cantor minimal subshifts abstract it is well known that a simple graph c algebra is either af or purely infinite in this paper we address the question of whether this is the case for labeled graph c algebras which include all graph c algebras and matsumoto algebras of subshifts there have been various c algebra constructions associated with subshifts and some of them are known to have the crossed products c x t z of cantor minimal subshifts x t as their quotient algebras we show that such a simple crossed product c x t z can be realized as a labeled graph c algebra since this c algebra is known to be an a t algebra and has z as its k 1 group our result provides a family of simple finite non af unital labeled graph c algebras

nest representations of directed graph algebras this paper is a comprehensive study of the nest representations for the free semigroupoid algebra mathfrak l g of a countable directed graph g as well as its norm closed counterpart the tensor algebra mathcal t g we prove that the finite dimensional nest representations separate the points in mathfrak l g and a fortiori in mathcal t g the irreducible finite dimensional representations separate the points in mathfrak l g if and only if g is transitive in components which is equivalent to being semisimple also the upper triangular nest representations separate points if and only if for every vertex x in mathcal t g supporting a cycle x also supports at least one loop edge we also study faithful nest representations we prove that mathfrak l g or mathcal t g admits a faithful irreducible representation if and only if g is strongly transitive as a directed graph more generally we obtain a condition on g which is equivalent to the existence of a faithful nest representation we also give a condition that determines the existence of a faithful nest representation for a maximal type mathbb n nest

simple labeled graph c algebras are associated to disagreeable labeled spaces abstract by a labeled graph c algebra we mean a c algebra associated to a labeled space e l e consisting of a labeled graph e l and the smallest normal accommodating set e of vertex subsets every graph c algebra c e is a labeled graph c algebra and it is well known that c e is simple if and only if the graph e is cofinal and satisfies condition l bates and pask extend these conditions of graphs e to labeled spaces and show that if a set finite and receiver set finite labeled space e l e is cofinal and disagreeable then its c algebra c e l e is simple in this paper we show that the converse is also true

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

constructing minimal homeomorphisms on point like spaces and a dynamical presentation of the jiang su algebra the principal aim of this paper is to give a dynamical presentation of the jiang su algebra originally constructed as an inductive limit of prime dimension drop algebras the jiang su algebra has gone from being a poorly understood oddity to having a prominent positive role in george elliott s classification programme for separable nuclear c algebras here we exhibit an etale equivalence relation whose groupoid c algebra is isomorphic to the jiang su algebra the main ingredient is the construction of minimal homeomorphisms on infinite compact metric spaces each having the same cohomology as a point this construction is also of interest in dynamical systems any self map of an infinite compact space with the same cohomology as a point has lefschetz number one thus if such a space were also to satisfy some regularity hypothesis which our examples do not then the lefschetz hopf theorem would imply that it does not admit a minimal homeomorphism

the structure of gauge invariant ideals of labelled graph c algebras abstract in this paper we consider the gauge invariant ideal structure of a c algebra c e l b associated to a set finite receiver set finite and weakly left resolving labelled space e l b where l is a labelling map assigning an alphabet to each edge of the directed graph e with no sinks it is obtained that if an accommodating set b is closed under relative complements there is a one to one correspondence between the set of all hereditary saturated subsets of b and the gauge invariant ideals of c e l b for this we introduce a quotient labelled space e l b r arising from an equivalence relation r on b and show the existence of the c algebra c e l b r generated by a universal representation of e l b r finally we give necessary and sufficient conditions for simplicity of certain labelled graph c algebras

topological entropy and the af core of a graph c algebra abstract let c e be the c algebra associated with a locally finite directed graph e and a e be the af core of c e for the topological entropy ht e in the sense of brown voiculescu of the canonical completely positive map e on the graph c algebra it is known that if e is finite ht e ht e a e h b e h l e where h b e respectively h l e is the block respectively the loop entropy of e in case e is irreducible and infinite h l e ht e a e h b e t is known recently where e t is the graph e with the edges directed reversely then by monotonicity of entropy h l e ht e is clear in this paper we show that ht e h b e t holds for locally finite infinite graphs e the af core a e is known to be stably isomorphic to the graph c algebra c e c z of certain skew product e c z and we also show that ht e c z ht e a e examples e p p 1 of irreducible graphs with ht e p log p are discussed

strength of convergence in the orbit space of a groupoid abstract let g be a second countable locally compact hausdorff groupoid with a haar system and let x n be a sequence in the unit space g 0 of g we show that the notions of strength of convergence of x n in the orbit space g 0 g and measure theoretic accumulation along the orbits are equivalent ways of realising multiplicity numbers associated to a sequence of induced representation of the groupoid c algebra

crossed products of the cantor set by free minimal actions of ℤd let d be a positive integer let x be the cantor set and let d act freely and minimally on x we prove that the crossed product c d x has stable rank one real rank zero and cancellation of projections and that the order on k0 c d x is determined by traces we obtain the same conclusion for the c algebras of various kinds of aperiodic tilings

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

the primitive ideals of the cuntz krieger algebra of a row finite higher rank graph with no sources abstract we catalogue the primitive ideals of the cuntz krieger algebra of a row finite higher rank graph with no sources each maximal tail in the vertex set has an abelian periodicity group of finite rank at most that of the graph the primitive ideals in the cuntz krieger algebra are indexed by pairs consisting of a maximal tail and a character of its periodicity group the cuntz krieger algebra is primitive if and only if the whole vertex set is a maximal tail and the graph is aperiodic

every classifiable simple c algebra has a cartan subalgebra we construct cartan subalgebras in all classifiable stably finite c algebras together with known constructions of cartan subalgebras in all uct kirchberg algebras this shows that every classifiable simple c algebra has a cartan subalgebra

on c algebras associated with c correspondences abstract we study c algebras arising from c correspondences which were introduced by the author we prove the gauge invariant uniqueness theorem and obtain conditions for our c algebras to be nuclear exact or satisfy the universal coefficient theorem we also obtain a 6 term exact sequence of k groups involving the k groups of our c algebras

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

finite digraphs and kms states abstract the paper contains a description of the kms states of a generalized gauge action on the c algebra of a finite graph

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

a generalized cuntz krieger uniqueness theorem for higher rank graphs we present a uniqueness theorem for k graph c algebras that requires neither an aperiodicity nor a gauge invariance assumption specifically we prove that for the injectivity of a representation of a k graph c algebra it is sufficient that the representation be injective on a distinguished abelian c subalgebra a crucial part of the proof is the application of an abstract uniqueness theorem which says that such a uniqueness property follows from the existence of a jointly faithful collection of states on the ambient c algebra each of which is the unique extension of a state on the distinguished abelian c subalgebra

algebraic cuntz pimsner rings from a system consisting of a ring r ap air ofr bimodules q and p and an r bimodule homomorphism p q r we construct a z graded ring t p q called the toeplitz ring and for certain systems a z graded quotient o p q of t p q called the cuntz pimsner ring these rings are the algebraic analogues of the toeplitz c algebra and the cuntz pimsner c algebra associated to a c correspondence also called a hilbert bimodule this new construction generalizes for example the algebraic crossed product by a single automorphism fractional skew monoid rings by a single corner automorphism and leavitt path algebras we also describe the structure of the graded ideals of our graded rings in terms of pairs of ideals of the coefficient ring and show that our cuntz pimsner rings satisfy the graded uniqueness theorem

semigroups of non unital endomorphisms of c algebras and compact group duality we show that the fixed point algebra og of the cuntz algebra on n 2 3 under the canonical action of a strongly compact group g of unitaries on the generating hubert space h is simple if the defining representation of g is a direct sum of finite dimensional representations whose determinant takes values in finite subgroups of the circle we use this result to define the doplicher roberts cross product of a unital c algebra a with centre cl by a semigroup of not necessarily unital endomorphisms generated by a countable orthogonal collection p i i n fulfilling natural conditions as an application we give necessary and sufficient conditions in order that a p is isomorphic to o g with the regular representation of a compact and metrizable group g and the set of endomorphisms induced by an irreducible decomposition of

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