compact lie group action with the continuous rokhlin property abstract in this paper we study the continuous rokhlin property of c dynamical systems using techniques of equivariant kk theory and quantum group theory in particular we determine the kk equivalence class and give a classification of kirchberg g algebras when the g is a compact lie group with the hodgkin condition

homology for operator algebras i spectral homology for reflexive algebras a stable homology theory is defined for completely distributive csl algebras in terms of the point neighbourhood homology of the partially ordered set of meet irreducible elements of the invariant projection lattice this specialises to the simplicial homology of the underlying simplicial complex in the case of a digraph algebra these groups are computable and useful in particular it is shown that if the first spectral homology group is trivial then schur automorphisms are automatically quasispatial this motivates the introduction of essential hochschild cohomology which we define by using the point weak star closure of coboundaries in place of the usual coboundaries

classification ofc algebras of real rank zero and unsuspendede equivalence types abstract in this article examples are given to prove that the graded scaled ordered k group is not the complete invariant for a c algebra in the class of unital separable nuclear c algebras of real rank zero and stable rank one even for a c algebra in the subclass which consists of those real rank zero stable rank one c algebras being expressed as inductive limits of k n i 1 m n i c x n i where x n i are two dimensional finite cw complexes and n i are positive integers in the case of simple such c algebras it has been proved that the above invariant is the complete invariant by george elliott and the author these examples prove that the classification conjecture of elliott for the case of non simple real rank zero c algebras should be revised one needs extra invariants the obstruction preventing two such c algebras with the same graded scaled ordered k group from being isomorphic is that they have different unsuspended e equivalence types a refinement of kk equivalence type of c algebras due to connes and higson in this article it is proved that for the above class of inductive limit c algebras the obstruction of unsuspended e equivalence type is the only obstruction i e if two c algebras in the class are unsuspended e equivalence then they are isomorphic it is a surprise that in the case of simple such c algebras or even the case of c algebras with finitely many ideals the obstruction will disappear see section 4

integrability and the ads cft correspondence in this paper we review the recently discovered asymptotic integrability in the planar sym theory and discuss its breakdown beyond the asymptotic region due to the wrapping interactions we also discuss novel dynamical tests of the ads cft correspondence one can perform in the special cases when the wrapping interactions may be neglected

order preservation in limit algebras abstract the matrix units of a digraph algebra a induce a relation known as the diagonal order on the projections in a masa in the algebra normalizing partial isometries in a act on these projections by conjugation they are said to be order preserving when they respect the diagonal order order preserving embeddings in turn are those embeddings which carry order preserving normalizers to order preserving normalizers this papers studies operator algebras which are direct limits of finite dimensional algebras with order preserving embeddings we give a complete classification of direct limits of full triangular matrix algebras with order preserving embeddings we also investigate the problem of characterizing algebras with order preserving embeddings

theory of strongly irreducible operators and its applications in the matrix theory of finite dimensional space the famous jordan canonical form theorem sufficiently reveals the internal structure of matrices in the survey we will give similar jordan canonical form theorems of operator theory in a complex separable infinite dimensional hilbert space by the way we also show their applications in other mathematical branches

the generalized berg theorem and bdf theorem let a be a separable simple af algebra with finitely many extreme traces we give a necessary and sufficient condition for an essentially normal element x e m a i e ir x is normal r m a m a a is the quotient map having the form y a for some normal element y c m a and a e a we also show that a normal element x e m a can be quasidiagonalized if and only if the fredholm index ind a x 0 for all a 0 sp 7r x in the case that a is a simple c algebra of real rank zero with stable rank one and with continuous scale k1 a 0 and ko a has countable rank we show that a normal element x e m a with zero fredholm index can be written as

on conjugacy of masas and the outer automorphism group of the cuntz algebra we investigate the structure of the outer automorphism group of the cuntz algebra and closely related with this problem of conjugacy of masaa in on in particular we exhibit an uncountable family of masas conjugate to the standard masa dn via bogolubov automorphisms that are not inner conjugate to dn

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

homogeneity of the pure state space of the cuntz algebra abstract if 1 2 are two pure gauge invariant states of the cuntz algebra o d we show that there is an automorphism of o d such that 1 2 if is a general pure state on o d and 0 is a given cuntz state we show that there exists an endomorphism of o d such that 0

endomorphisms of o n which preserve the canonical uhf subalgebra abstract unital endomorphisms of the cuntz algebra o n which preserve the canonical uhf subalgebra f n o n are investigated we give examples of such endomorphisms u for which the associated unitary element u in o n which satisfies s j u s j for all j does not belong to f n one such example in the case where n 2 arises from a construction of a unital endomorphism on o 2 which preserves the canonical uhf subalgebra and where the relative commutant of its image in o 2 contains a copy of o 2

lie isomorphisms of reflexive algebras a lie isomorphism between algebras is called trivial if where is an algebraic isomorphism or a negative of an algebraic anti isomorphism and is a linear map with image in the center vanishing on each commutator in this paper we investigate the conditions for the triviality of lie isomorphisms from reflexive algebras with completely distributive and commutative lattices cdcsl in particular we prove that a lie isomorphism between irreducible cdcsl algebras is trivial if and only if it preserves i idempotent operators the sum of an idempotent and a scalar multiple of the identity in both directions we also prove the triviality of each lie isomorphism from a cdcsl algebra onto a csl algebra which has a comparable invariant projection with rank and corank not one some examples of lie isomorphisms are presented to show the sharpness of the conditions

finite element analysis of contact between elastic self affine surfaces finite element methods are used to study nonadhesive frictionless contact between elastic solids with self affine surfaces we find that the total contact area rises linearly with the load at small loads the mean pressure in the contact regions is independent of load and proportional to the root mean square slope of the surface the constant of proportionality is nearly independent of the poisson ratio and roughness exponent and lies between previous analytic predictions the contact morphology is also analyzed connected contact regions have a fractal area and perimeter the probability of finding a cluster of area a c drops as a tau c where tau increases with a decrease in roughness exponent the distribution of pressures shows an exponential tail that is also found in many jammed systems these results are contrasted to simpler models and experiments

approximately finitely acting operator algebras let e be an operator algebra on a hilbert space with finite dimensional c algebra c e a classification is given of the locally finite algebras a0 formula ak k and the operator algebras a formula ak k obtained as limits of direct sums of matrix algebras over e with respect to star extendible homomorphisms the invariants in the algebraic case consist of an additive semigroup with scale which is a right module for the semiring ve homu e e of unitary equivalence classes of star extendible homomorphisms this semigroup is referred to as the dimension module invariant in the operator algebra case the invariants consist of a metrized additive semigroup with scale and a contractive right module ve action subcategories of algebras determined by restricted classes of embeddings such as 1 decomposable embeddings between digraph algebras are also classified in terms of simplified dimension modules

the algebraic curve of classical superstrings on ads5 s5 we investigate the monodromy of the lax connection for classical iib superstrings on ads5 s5 for any solution of the equations of motion we derive a spectral curve of degree 4 4 the curve consists purely of conserved quantities all gauge degrees of freedom have been eliminated in this form the most relevant quantities of the solution such as its energy can be expressed through certain holomorphic integrals on the curve this allows for a classification of finite gap solutions analogous to the general solution of strings in flat space the role of fermions in the context of the algebraic curve is clarified finally we derive a set of integral equations which reformulates the algebraic curve as a riemann hilbert problem they agree with the planar one loop open image in new window supersymmetric gauge theory proving the complete agreement of spectra in this approximation

almost commuting unitaries and classification of purely infinite simplec algebras we show that for any irrational rotational algebraa a o2 o2 this is proved by combining recently established results forc algebras of real rank zero with the following result for anye 0 there is 0 such that for any pair of unitariesu vin any purely infinite simplec algebraawithk1 a 0 satisfies uv vu and u v 0 there is a pair of commuting unitariesu v awith finite spectrum such that u u eand v v e more general results concerning almost commuting unitaries are also obtained

classification of simple c algebras with unique traces we classify certain almost multiplicative morphisms up to approximate unitary equivalence and use this result to prove the following let a and b be two unital separable simple c algebras of real rank zero stable rank one with weakly unperforated k 0 groups and with unique normalized quasi traces suppose that both a and b are locally ah and k a k a 1 a k b k b 1 b then a is isomorphic to b

the lattice of ideals of a triangular af algebra we study triangular af taf algebras in terms of their lattices of closed two sided ideals not isometrically isomorphic taf algebras can have isomorphic lattices of ideals indeed there is an uncountable family of pairwise non isomorphic algebras all with isomorphic lattices of ideals in the positive direction if a and b are strongly maximal taf algebras with isomorphic lattices of ideals then there is a bijective isometry between the subalgebras of a and b generated by their order preserving normalizers this bijective isometry is the sum of an algebra isomorphism and an anti isomorphism using this we show that if the taf algebras are generated by their order preserving normalizers and are triangular subalgebras of primitive c algebras then the lattices of ideals are isomorphic if and only if the algebras are either isometrically isomorphic or anti isomorphic finally we use complete distributivity to show that there are taf algebras whose 0 lattices of ideals can not arise from taf algebras generated by their order preserving 8 normalizers our techniques rely on constructing a topological binary relation based on the lattice of ideals this relation is closely connected to the spectrum or fundamental relation also a topological binary relation of the taf algebra

finite group actions on c algebras with the rohlin property i basic properties of finite group actions with the rohlin property on unital c algebras are investigated a characterization of finite group actions with the rohlin property on the cuntz algebra 02 is given in terms of central sequences which may be considered as an equivariant version of e kirchberg and n c phillips s characterization of 02 a large class of symmetries on 02 are classified in terms of the fixed point algebras for conjugacy and the crossed products for cocycle conjugacy model actions of symmetries of 02 are constructed for given k theoretical invariants

decomposable approximations of nuclear c algebras abstract we show that nuclear c algebras have a refined version of the completely positive approximation property in which the maps that approximately factorize through finite dimensional algebras are convex combinations of order zero maps we use this to show that a separable nuclear c algebra a which is closely contained in a c algebra b embeds into b

the nuclear dimension of c algebras abstract we introduce the nuclear dimension of a c algebra this is a noncommutative version of topological covering dimension based on a modification of the earlier concept of decomposition rank our notion behaves well with respect to inductive limits tensor products hereditary subalgebras hence ideals quotients and even extensions it can be computed for many examples in particular it is finite for all uct kirchberg algebras in fact all classes of nuclear c algebras which have so far been successfully classified consist of examples with finite nuclear dimension and it turns out that finite nuclear dimension implies many properties relevant for the classification program surprisingly the concept is also linked to coarse geometry since for a discrete metric space of bounded geometry the nuclear dimension of the associated uniform roe algebra is dominated by the asymptotic dimension of the underlying space

type iii representations and automorphisms of some separable nuclear c algebras abstract powers proved decades ago that if two cyclic representations 1 and 2 of a uhf algebra a satisfy that 1 a 2 a m there is an automorphism of a such that 1 and 2 are quasi equivalent this was recently extended to the class of simple separable c algebras when m is of type i in this paper we extend this result to some class of simple separable nuclear c algebras when m is of type iii in particular we show that the above result obtained by powers for the uhf algebras also holds for the class of purely infinite simple separable c algebras classified by kirchberg and phillips and for the class of approximately homogeneous simple separable unital c algebra with unique tracial state

homology for operator algebras ii stable homology for non self adjoint algebras new homology groups are defined for a non self adjoint operator algebra with a distinguished masa which is based upon cycles and boundaries associated with complexes of partial isometries in the stable algebra under natural hypotheses the zeroth order group coincides with thek0group of the generatedc algebra several identifications and applications are given and in particular it is shown how stable homology is significant for the classification of regular subalgebras and regular limit algebras

higher dimensional virtual diagonals and ideal cohomology for triangular algebras we investigate the cohomology of non self adjoint algebras using virtual diagonals and their higher dimensional generalizations we show that infinite dimensional nest algebras always have non zero second cohomology by showing that they cannot possess 2 virtual diagonals in the case of the upper triangular atomic nest algebra we exhibit concrete modules for non vanishing cohomology

from infinitesimal to full contact between rough surfaces evolution of the contact area we carry out a statistically meaningful study on self affine rough surfaces in elastic frictionless non adhesive contact we study the evolution of the true contact area under increasing squeezing pressure from zero up to full contact which enables us to compare the numerical results both with asperity based models at light pressures and with persson s contact model for the entire range of pressures a good agreement of numerical results with persson s model is obtained for the shape of the area pressure curve especially near full contact however we obtain qualitatively different results for its derivative at light pressures we investigate the effects of the longest and shortest wavelengths in surface spectrum which control the surface gaussianity and spectrum breadth nayak s parameter we revisit the influence of nayak s parameter which is frequently assumed to play an important role in mechanics of rough contact

integrability test for spin chains we examine a simple heuristic test of integrability for quantum chains this test is applied to a variety of systems including isotropic spin 1 models with nearest neighbour interaction potts type inhomogeneous spin 1 2 chains and a multiparameter family of spin 1 2 models generalizing the xyz chain with next to nearest neighbour interactions and bond alternation within the latter family we determine all the integrable models with an o 2 symmetry

isomorphisms between leavitt algebras and their matrix rings let k be any field let ln denote the leavitt algebra of type 1 n 1 hav ing coe cients in k and let md ln denote the ring of dd matrices over ln in our main result we show that md ln g ln if and only if d and n 1 are coprime we use this isomorphism to answer a question posed in 14 regarding isomorphisms between various c algebras furthermore our result demonstrates that data about the k0 structure is suf ficient to distinguish up to isomorphism the algebras in an important class of purely infinite simple k algebras

relative positions of matroid algebras abstract a classification is given for regular positions d d d of jones index 4 where equation omitted is an even matroid algebra and where the individual summands have index 2 a similar classification is obtained for positions of direct sums of 2 symmetric algebras and in the odd case for the positions of sums of 2 symmetric c algebras in matroid c algebras the approach relies on an analysis of intermediate non self adjoint operator algebras and the classifications are given in terms of k0 invariants partial isometry homology and scales in the composite invariant k0 h1

homology for operator algebras abstract a 4 cycle algebra is a finite dimensional digraph algebra csl algebra whose reduced digraph is a 4 cycle a rigid embedding between such algebras is a direct sum of certain nondegenerate multiplicity one star extendible embeddings a complete classification is obtained for the regular isomorphism classes of direct systems a of 4 cycle algebras with rigid embeddings the critical invariant is a binary relation in k 0 a h 1 a generalising the scale of the k 0 group called the joint scale the joint scale encapsulates other invariants and compatibility conditions of regular isomorphism these include the scale of h 1 a the scale of h 0 a h 1 a sign compatibility congruence compatibility and h 0 h 1 coupling classes these invariants are also important for lifting k 0 h 1 isomorphisms to algebra isomorphisms we resolve this lifting problem for various classes of 4 cycle algebra direct systems

semilattices of groups and inductive limits of cuntz algebras we characterize in terms of elementary properties the abelian monoids which are direct limits of finite direct sums of monoids of the form z nz cup 0 where 0 is a new zero element for positive integers n the key properties are the riesz refinement property and the requirement that each element x has finite order that is n 1 x x for some positive integer n such monoids are necessarily semilattices of abelian groups and part of our approach yields a characterization of the riesz refinement property among semilattices of abelian groups further we describe the monoids in question as certain submonoids of direct products lambda times g for semilattices lambda and torsion abelian groups g when applied to the monoids v a appearing in the non stable k theory of c algebras our results yield characterizations of the monoids v a for c inductive limits a of sequences of finite direct products of matrix algebras over cuntz algebras o n in particular this completely solves the problem of determining the range of the invariant in the unital case of r o rdam s classification of inductive limits of the above type

almost commuting unitary elements in purely infinite simple c algebras we consider the problem whether a pair of almost commuting unitaries selfadjoints is close to a pair of commuting unitaries selfadjoints it is an old problem see hi psh bo v1 v2 d bd ch lorl exli exl2 de lin4 etc dan voiculescu showed in v2 that there is a positive number d and a sequence of commuting unitary matrices un and v with i u v v u ji o

the restricted weyl group of the cuntz algebra and shift endomorphisms it is shown that modulo the automorphisms which fix the canonical diagonal masa point wise the group of those automorphisms of on which globally preserve both the diagonal and the core uhf subalgebra is isomorphic via restriction with the group of those homeomorphisms of the full one sided n shift space which eventually commute along with their inverses with the shift transformation the image of this group in the outer automorphism group of on can be embedded into the quotient of the automorphism group of the full two sided n shift by its center generated by the shift if n is prime then this embedding is an isomorphism msc 2010 46l40 37b10

thermodynamic bethe ansatz for planar ads cft a proposal moving from the mirror theory bethe yang equations proposed by arutyunov and frolov we derive the thermodynamic bethe ansatz equations which should control the spectrum of the planar ads5 cft4 correspondence the associated set of universal functional relations y system satisfied by the exponentials of the tba pseudoenergies is deduced confirming the structure inferred by gromov kazakov and vieira

cohomology for operator algebras the mayer vietoris sequence abstract for an inclusion b a of operator algebras we introduce the b nil cohomology groupshn a b which can be easier to compute than the standard cohomology groupshn a we then develop two long exact sequences the first linkinghn a b hn a andhn b the second corresponding to the mayer vietoris sequence of algebraic topology these sequences provide powerful computational tools as illustrated by the examples in the last two sections of the paper

an approximate universal coefficient theorem an approximate universal coefficient theorem auct for certain c algebras is established we present a proof that kirchberg phillips s classification theorem for separable nuclear purely infinite simple c algebras is valid for c algebras satisfying the auct instead of the uct it is proved that two versions of auct are in fact the same we also show that c algebras that are locally approximated by c algebras satisfying the auct satisfy the auct as an application we prove that certain simple c algebras which are locally type i are in fact isomorphic to simple ah algebras as another application we show that a sequence of residually finite dimensional c algebras which are asymptotically nuclear and which asymptotically satisfies the auct can be embedded into the same simple af algebra

incipient sliding of rough surfaces in contact a multiscale numerical analysis in this paper the cattaneo theory of frictional contact is extended to elastic half spaces in contact through rough disordered interfaces the discrete version of the cattaneo theorem is provided and represents the basis of a multiscale numerical contact algorithm mathematical surfaces with imposed roughness as well as experimentally digitised ones are analysed by means of a numerical method the evolution of the contact domain at different resolution is investigated roughness of the interfaces provides lacunarity of the contact domains whose fractal dimension is always smaller than 2 0 when a tangential force is applied the extent of the stick area decreases in the same way as the contact area develops with increasing pressure and the slip area is found to be proportional to the tangential force as predicted by cattaneo theory the evolution of the shear centroid as well as the amount of dissipated energy up to full sliding are provided finally it is shown that at a sufficient level of discretization the distribution of contact pressures is multifractal

algebraic curve for the so 6 sector of ads cft we construct the general algebraic curve of degree four solving the classical sigma model on s 5 up to two loops it coincides with the algebraic curve for the dual sector of scalar operators in open image in new window sym also constructed here

the dressing factor and crossing equations we utilize the dhm integral representation for the bes dressing factor of the world sheet s matrix of the ads5 s5 light cone string theory and the crossing equations to fix the principal branch of the dressing factor on the rapidity torus the results obtained are further used in conjunction with the fusion procedure to determine the bound state dressing factor of the mirror theory we convincingly demonstrate that the mirror bound state s matrix found in this way does not depend on the internal structure of a bound state solution employed in the fusion procedure this welcome feature is in perfect parallel to string theory where the corresponding bound state s matrix has no bearing on bound state constituent particles as well the mirror bound state s matrix we found provides the final missing piece in setting up the tba equations for the ads5 s5 mirror theory

using green s function molecular dynamics to rationalize the success of asperity models when describing the contact between self affine surfaces we use green s function molecular dynamics to evaluate the effectiveness of asperity models when describing the contact mechanics of elastic solids with self affine surfaces surfaces are created with the help of a fourier filtering algorithm and the interactions between the solids are modeled via hard wall potentials we illustrate how the real area of contact a real is formed by a set of contact clusters two different regimes are identified when the normal force per cluster l c is plotted as a function of its area a c small clusters satisfy a hertzian type law l c approximately a c 32 while large clusters display a linear l c approximately a c behavior it is shown how the area a c where the crossover between the two regimes takes place depends only on the roughness at the smallest length scale if the longitudinal dimension of the surface remains unaltered moreover our results display a distribution of cluster sizes p a c remaining nearly constant for areas smaller than a c while showing power law decay above such a critical value furthermore we found the heights of the contacting atoms to be normally distributed with width inversely proportional to the surface roughness

the uniqueness of af diagonals in regular limit algebras necessary and sufficient conditions are obtained for the uniqueness of standard regular af maximal abelian self adjoint algebras in regular limit algebras up to approximate inner unitary equivalence

finite group actions on c algebras with the rohlin property ii abstract we classify finite group actions on some classes of c algebras with the rohlin property in terms of the k groups a group cohomological obstruction is obtained for the k groups of a c algebra allowing such an action for example the tate cohomology groups with the k groups as the coefficient modules must vanish model actions with the rohlin property are constructed for given k theoretical invariants quasi free actions of finite cyclic groups on the cuntz algebras and their dual actions are investigated from the view point of the rohlin property

on the cohomology of joins of operator algebras abstract by analogy with the join in topology the join a b for operator algebras a and b acting on hilbert spaces h and k respectively was defined by gilfeather and smith amer j math 116 1994 541 561 assuming that k is finite dimensional they calculated the hochschild cohomology groups for a b with coefficients in l k h we assume that a is a maximal abelian von neumann algebra acting on h a is a subalgebra of a l k and b is an ultraweakly closed subalgebra of m n a containing a 1 n we show that b may be decomposed into a finite sum of free modules in this context we redefine the join of a and b generalize the calculations of gilfeather and smith and calculate h m a b a l c n k for all m 0