cyclic homology comodules and mixed complexes relating cyclic and hochschild homology one can see that any formula for hc a a will not only involve hc a and hc a but also the periodicity operator s and the hochschild groups fortunately if the map s brings in some complications it also endows hc a with a comodule structure over the cyclic homology of the ground ring k actually the comodule structure exists already on the complex level a convenient complex on which s has the form of a canonical surjection is connes s double complex with differentials b and b now the idea is to view the cyclic homology of an algebra as a composite functor

cyclic homology of hopf crossed products abstract we obtain a mixed complex simpler than the canonical one given the hochschild cyclic negative and periodic homology of a crossed product e a f h where h is an arbitrary hopf algebra and f is a convolution invertible cocycle with values in a we actually work in the more general context of relative cyclic homology specifically we consider a subalgebra k of a which is stable under the action of h and we find a mixed complex computing the hochschild cyclic negative and periodic homology of e relative to k as an application we obtain two spectral sequences converging to the cyclic homology of e relative to k the first one works in the general setting and the second one which generalizes those previously found by several authors works when f takes its values in k

a differential complex for poisson manifolds construction du complexe canonique d une variete de poisson homologie canonique des varietes symplectiques application a l homologie de hochschild des algebres non commutatives

cyclic cohomology for graded c r c r algebras and its pairings with van daele k theory we consider cycles for graded c mathfrak r algebras real c algebras which are compatible with the structure and the real structure their characters are cyclic cocycles we define a connes type pairing between such characters and elements of the van daele k groups of the c mathfrak r algebra and its real subalgebra this pairing vanishes on elements of finite order we define a second type of pairing between characters and k group elements which is derived from a unital inclusion of c algebras it is potentially non trivial on elements of order two and torsion valued such torsion valued pairings yield topological invariants for insulators the two dimensional kane mele and the three dimensional fu kane mele strong invariant are special cases of torsion valued pairings we compute the pairings for a simple class of periodic models and establish structural results for two dimensional aperiodic models with odd time reversal invariance

noncommutative residues and manifolds with conical singularities abstract for every singular point on a manifold with conical singularities a trace can be constructed on the cone algebra with asymptotics introduced by b w schulze each of them vanishes on operators supported in the interior and is therefore different from the noncommutative residue established by wodzicki on the ideal of operators with zero conormal symbol however we find another trace which coincides with the noncommutative residue in the interior all these traces are shown to be essentially unique on a slightly extended version of the cone algebra

nil k theory maps to cyclic homology algebraic k theory breaks into two pieces nil k theory and karoubi villamayor k theory karoubi has constructed chern classes from the latter groups into cyclic homology we construct maps from nil k theory to cyclic homology which are compatible with karoubi s maps but with a degree shift several recent results show that in characteristic zero our map is often an isomorphism ever since a connes discovered cyclic homology in 1982 it has been widely held that cyclic homology is closely related to algebraic k theory supporting this belief karoubi defined chern classes limep kn a limhcn 2p a in k1 and goodwillie defined a related map ey kn a hcn a in g other maps between k theory and variants of cyclic homology have been constructed by loday unpublished burghelea bur 1 ogle ogle 1 and others of course all of these maps are related to the dennis trace map to hochschild homology d kn a hhn a which r k dennis discovered in 1975 d in this paper we prove three results the first is that karoubi s map factors through goodwillie s theorem a for every associative algebra there is a commutative diagram kn a

the cohomology of monogenic extensions in the noncommutative setting abstract we study the hochschild and cyclic homology of noncommutative monogenic extensions as an application we compute the hochschild and cyclic homology of the rank 1 hopf algebras introduced in l krop d radford finite dimensional hopf algebras of rank 1 in characteristic 0 journal of algebra 302 1 2006 214 230

cyclic cohomology and the family lefschetz theorem any closed current on the base of a compact fibration gives rise to a cyclic cocycle on the smooth convolution algebra we prove that such cocycle furnishes additive maps from the vertically equivariant k theory to the scalars this enables to associate to any closed current on the base of the fibration a lefschetz formula for fiber preserving isometries using geometric operators on the base we deduce the integrality of some characteristic numbers

boundary maps for c crossed products with r with an application to the quantum hall effect the boundary map in k theory arising from the wiener hopf extension of a crossed product algebra with r is the connes thom isomorphism in this article the wiener hopf extension is combined with the heisenberg group algebra to provide an elementary construction of a corresponding map on higher traces and cyclic cohomol ogy it then follows directly from a non commutative stokes theorem that this map is dual w r t connes pairing of cyclic cohomology with k theory as an application we prove equality of quantized bulk and edge conductivities for the integer quantum hall effect described by continuous magnetic schrodinger operators 1 motivation and main result in a commonly used approach to study aperiodic solids particles in the bulk of the medium are described by covariant families of one particle schrodinger operators h whereis the probability space of configurations furnished with an ergodic action of space translations crossed product algebras provide a natural framework for such families be86 in particular their bounded functions are represented by elements of a c crossed product the so called bulk algebra the non commutative topology of the c algebra is a useful tool to construct topological invariants resulting from pairings between k group elements and higher traces some of these invariants may be physi cally interpreted as topologically quantised quantities the quantised hall conductivity is such an example the physics near a boundary of the solid can also be described by a c algebra the so called edge algebra the bulk algebra being essentially a crossed product of the edge algebra with r or with z in the tight binding approximation krs02 both algebras are tied together in the wiener hopf extension or respectively the toeplitz extension this extension gives rise to boundary maps between the k groups and the higher traces of the bulk and edge algebra which allow one to equate bulk and edge in variants this topological relation and its physical interpretations is our main objective we discuss one prominent physical example of this the quantum hall effect where the

central extension of quadratic lie algebras and its relation to dihedral homology if a is a k algebra where k is a commutative ring then kassel and w x w x loday in 5 study sl a s gl a gl a where gl a is the lie n n n n algebra of n n matrices over a they define a steinberg lie algebra st a which they prove is a universal central lie algebra extension of n sl a furthermore the kernel of this extension is isomorphic to a cyclic n homology group which in our current notation is designated as hc a 1 in this paper we prove a similar result for a a k algebra with involution a a a which acts trivially on k given a form parameter l and l g center a such that ll s 1 we have a form algebra a l l see w x 1 the lie algebra adaptation of the general l quadratic group gq a l will be denoted as gq l and will be a sub lie algebra of 2 n 2 n gl a we will show that the commutator subalgebra of gq l does not 2 n 2 n depend on the choice of parameter l this subalgebra will be denoted as sq a and will be called the special quadratic lie algebra of a there is 2 n another subalgebra sq l which does depend on the choice of l we 2 n

a class of equilibrium problems with lower and upper bounds abstract in this paper we obtained some existence results of a class of abstract equilibrium problem our results give answers to the open problem raised by isac et al furthermore we studied the equilibrium problems with lower and upper bounds and restricted conditions and obtained more results finally we generalized these open problems to the case of two spaces

index theory for quasi crystals i computation of the gap label group abstract in this paper we give a complete solution to the gap labelling conjecture for quasi crystals the method adopted relies on the index theory for laminations and the main tools are the connes skandalis longitudinal k theory index morphism together with the measured index formula

a homology theory for etale groupoids etale groupoids arise naturally as models for leaf spaces of foliations for orbifolds and for orbit spaces of discrete group actions in this paper we introduce a sheaf homology theory for etale groupoids we prove its invariance under morita equivalence as well as verdier duality between haeiger cohomology and this homology we also discuss the relation to the cyclic and hochschild homologies of connes convolution algebra of the groupoid and derive some spectral sequences which serve as a tool for the computation of these homologies

a new proof of weyl s formula on the asymptotic distribution of eigenvalues one of the more perplexing problems of finite particle quantum mechanics is to find the appropriate quantum mechanical description of a given classical mechanical system unfortunately from the mathematical point of view this problem is not terribly well posed suppose the classical system in question is represented by a symplectic manifold x and a classical observable p x r suppose also for simplicity that this system is a confined system in the sense that the sets p 1 are all compact let h be a hilbert space and let p be a self adjoint operator on h representing a quantum observable without specifying anything further about p for instance its relation to other observables there is practically no way of ascertaining whether p is an appropriate quantum counterpart of p at first glance the only requirements this appears to impose on p are that the spectrum of p be discrete and that the number of eigenvalues n a less than 1 be finite for all 1 this is the analogue of the condtion that p 1 be compact by examining the statistical properties of a large aggregate of classical systems each a copy of x p one can in fact say a little bit more about the relation p to p by comparing classical and quantum partition functions one can show that for iz large

integrability of lie brackets in this paper we present the solution to a longstanding problem of differential geometry lie s third theorem for lie algebroids we show that the integrability problem is controlled by two computable obstructions as applications we derive explain and improve the known integrability results we establish integrability by local lie groupoids we clarify the smoothness of the poisson sigma model for poisson manifolds and we describe other geometrical applications

existence of solutions for abstract economic equilibrium problems and algorithm in this paper we study a new kind of vector equilibrium problem and we proved the existence of solutions for this kind of equilibrium problem by using the section theorem and fan kkm theorem then we generalize this kind of vector equilibrium problem to a more general case equilibrium problems with lower and upper bounds was an open problem proposed by isac sehgal and singh in 1999 j li o chadli y chiang and j c yao zhang cong jun derived some results of the equilibrium problems with lower and upper bounds under certain conditions in this paper we derive more results of this open problem under certain conditions constructs an iteration algorithm and discuses the convergence of the algorithm

pseudodifferential operators on supermanifolds and the atiyah singer index theorem fermionic quantization or clifford algebra is combined with pseudodifferential operators to simplify the proof of the atiyah singer index theorem for the dirac operator on a spin manifold

the dimension formula of the cyclic homology of truncated quiver algebras over a field of positive characteristic abstract we give the dimension formula of the cyclic homology of truncated quiver algebras over a field of positive characteristic this is done by using a mixed complex due to cibils we consider a spectral sequence associated with the cibils mixed complex which converges to the cyclic homology the e 1 term of this spectral sequence that is the hochschild homology is calculated by skoldberg in this paper by means of chain maps between the projective resolution constructed by skoldberg and one by cibils we calculate the e 2 term and we have the dimension formula of the cyclic homology

the atiyah singer index formula for subelliptic operators on contact manifolds part i the atiyah singer index theorem gives a topological formula for the index of an elliptic differential operator the topological index depends on a cohomology class that is constructed from the principal symbol of the operator on contact manifolds the important fredholm operators are not elliptic but hypoelliptic their symbolic calculus is noncommutative and is closely related to analysis on the heisenberg group for a hypoelliptic differential operator in the heisenberg calculus on a contact manifold we construct a symbol class in the k theory of a noncommutative c algebra that is associated to the algebra of symbols there is a canonical map from this analytic k theory group to the ordinary cohomology of the manifold which gives a de rham class to which the atiyah singer formula can be applied we prove that the index formula holds for these hypoelliptic operators our methods derive from connes tangent groupoid proof of the index theorem

groupoids and an index theorem for conical pseudo manifolds we define an analytical index map and a topological index map for conical pseudomanifolds these constructions generalize the analogous constructions used by atiyah and singer in the proof of their topological index theorem for a smooth compact manifold m a main ingredient is a non commutative algebra that plays in our setting the role of c 0 t m we prove a thom isomorphism between non commutative algebras which gives a new example of wrong way functoriality in k theory we then give a new proof of the atiyah singer index theorem using deformation groupoids and show how it generalizes to conical pseudomanifolds we thus prove a topological index theorem for conical pseudomanifolds

superconformal algebras and clifford algebras it is shown that superconformal lie superalgebras contain a clifford algebra structure this is used to present a classification of these algebras under the following assumptions only fields with half integer conformal dimension between 2 and 1 2 and a nonzero central element it turns out that the number of supersymmetry generators must be less than or equal to 4 more generally the so n series as well as some nonassociative algebras connected to s7 also have a natural place in this clifford algebra framework

the cyclic homology of affine algebras in this paper we study the cyclic homology of affine algebras over a field of characteristic 0 we show that if a is such an algebra the inverse system hc 2m a s m decomposes in sufficiently large degrees into the direct h 2tta sum of the constant system with value mz inf and a system which is essentially zero the essentially zero component is the kernel of the loday quillen map l and the behavior of the restriction of s on it is closely related to the degeneracy of the spectral sequence associated with connes exact couple of a

the local structure of poisson manifolds varietes de poisson et applications decomposition structures de poisson lineaires approximation lineaire systemes hamiltoniens le probleme de linearisation groupes de fonction realisations et applications impulsion paires duales et groupes de jauge existence des realisations unicite des realisations les problemes des 3 corps restreints et autres exemples

new existence results for equilibrium problems we consider equilibrium problems in the framework of the formulation proposed by blum and oettli which includes variational inequalities nash equilibria in noncooperative games and vector optimization problems for instance as particular cases we establish new sufficient and or necessary conditions for existence of solutions of such problems our results are based upon the relation between equilibrium problems and certain auxiliary convex feasibility problems together with extensions to equilibrium problems of gap functions for variational inequalities then we apply our results to some particular instances of equilibrium problems obtaining results which include among others a new lemma of the alternative for convex optimization problems

the gysin triangle via localization and a 1 homotopy invariance the first author was partially supported by the nsf career award 1350472 and by the portuguese foundation for science and technology grant pest oe mat ui0297 2014

homology of algebras of families of pseudodifferential operators abstract we compute the hochschild cyclic and periodic cyclic homology groups of algebras of families of laurent complete symbols on manifolds with corners we show in particular that the spectral sequence associated with hochschild homology degenerates at e 2 and converges to hochschild homology as a byproduct we identify the space of residue traces on fibrations by manifolds with corners in the process we prove some structural results about algebras of complete symbols on manifolds with corners

tensor triangular geometry of non commutative motives abstract in this article we initiate the study of the tensor triangular geometry of the categories mot k a and mot k l of non commutative motives over a base ring k since the full computation of the spectrum of mot k a and mot k l seems completely out of reach we provide some information about the spectrum of certain subcategories more precisely we show that when k is a finite field or its algebraic closure the spectrum of the monogenic cores core k a and core k l i e the thick triangulated subcategories generated by the tensor unit is closely related to the zariski spectrum of z moreover we prove that if we slightly enlarge core k a to contain the non commutative motive associated to the ring of polynomials k t and assume that k is a field of characteristic zero then the corresponding spectrum is richer than the zariski spectrum of z

bicomplexes and conservation laws in non abelian toda models a bicomplex structure is associated with the leznov saveliev equation of integrable models the linear problem associated with the zero curvature condition is derived in terms of the bicomplex linear equation the explicit example of a non abelian conformal affine toda model is discussed in detail and its conservation laws are derived from the zero curvature representation of its equation of motion

on a hodge theoretic property of the kunneth map in periodic cyclic homology abstract we prove that the standard kunneth map in periodic cyclic homology of differential z 2 graded algebras is compatible with a generalization of the hodge filtration and explain how this result is related to various thom sebastiani type theorems in singularity theory

l homologie cyclique des algebres enveloppantes for any lie algebra g we compute the hochschild and cyclic homology groups of its enveloping algebra in terms of the canonical lie poisson structure on the dual g we also discuss the collapsing of connes spectral sequence for cyclic homology particularly in the case of semisimple lie algebras

cyclic homology of brzezinski s crossed products and of braided hopf crossed products abstract let k be a field a a unitary associative k algebra and v a k vector space endowed with a distinguished element 1 v we obtain a mixed complex simpler than the canonical one that gives the hochschild cyclic negative and periodic homologies of a crossed product e a f v in the sense of brzezinski we actually work in the more general context of relative cyclic homology specifically we consider a subalgebra k of a that satisfies suitable hypothesis and we find a mixed complex computing the hochschild cyclic negative and periodic homologies of e relative to k then when e is a cleft braided hopf crossed product we obtain a simpler mixed complex that also gives the hochschild cyclic negative and periodic homologies of e

the atiyah singer index theorem for families of dirac operators two heat equation proofs the purpose of this paper is to give two heat equation proofs of the index theorem of atiyah singer for a family of dirac operators

analytic k theory on manifolds with corners let y be a compact manifold in 1 atiyah proposed an analytic delinition of the k homology groups k y defined abstractly as the dual theory to the atiyah hirzebruch k cohomology theory these ideas were developed by kasparov 15 and brown douglas and fillmore lo cycles for this analytic k homology theory are abstract elliptic operators i e bounded linear operators between hilbert spaces satisfying additional conditions derived from the properties of elliptic pseudo differential operators in particular elliptic pseudodifferential operators between sections of vector bundles define such cycles the homology class of the cycle depends only on the principal symbol and indeed only on the k cohomology class it represents on the cotangent bundle in fact it had already been shown in essence by atiyah that the resulting map

type ii non commutative geometry i dixmier trace in von neumann algebras abstract we define the notion of connes von neumann spectral triple and consider the associated index problem we compute the analytic chern connes character of such a generalized spectral triple and prove the corresponding local formula for its hochschild class this formula involves the dixmier trace for ii von neumann algebras in the case of foliations we identify this dixmier trace with the corresponding measured wodzicki residue

excision in cyclic homology and in rational algebraic k theory for a precise definition see 1 below by replacing everywhere k by k q one obtains the corresponding notion in rational algebraic k theory the above definition has an obvious counterpart for cyclic homology and algebras over a fixed field in the case of a general commutative ground ring k some restrictions on the class of allowable extensions seem inevitable due to the well known limitations of cyclic homology considered as a homology functor for algebras not flat over a ground ring an extension of k algebras will be called pure if it is pure as an extension of k modules in the sense of p m cohn 6 cf also appendix a 3 below the class of pure extensions contains e g i extensions which admit a k module splitting ii extensions a e r s with s flat over k in fact one among the several possible characterizations of purity says that an extension is pure if and only if the underlying extension of k modules is an inductive limit of split extensions see theorem a 4 of appendix a below everywhere in this paper the word excision used in the context of cyclic homology will mean excision with respect to the class of pure extensions the second purpose of the present paper is to give a complete characterization of the class of algebras possessing the excision property in cyclic homology before stating the corresponding result we need the following definition let us

some existence theorems in nonlinear analysis for mappings on gfc spaces and applications abstract we establish a maximal element theorem an intersection theorem and a coincidence point theorem in product gfc spaces as examples of wide ranges of applications we first deduce sufficient conditions for the solution existence of a mixed system of inclusions then using this we obtain existence results for systems of vector quasi optimization problems and for multiobjective mathematical programs constrained by systems of inclusions our results are shown to improve and include recent ones in the literature

bicomplexes and backlund transformations a bicomplex is a simple mathematical structure in particular associated with completely integrable models the conditions defining a bicomplex are a special form of a parameter dependent zero curvature condition we generalize the concept of a darboux matrix to bicomplexes and use it to derive backlund transformations for several models the method also works for moyal deformed equations with a corresponding deformed bicomplex

k regularity cdh fibrant hochschild homology and a conjecture of vorst it is a well known fact that algebraic if theory is homotopy invariant as a functor on regular schemes if x is a regular scheme then the natural map kn x kn x x 1 is an isomorphism for all n ez this is false in general for nonregular schemes and rings to express this failure bass introduced the terminology that for any contravari ant functor v defined on schemes a scheme x is called v regular if the pullback maps v x v x x ar are isomorphisms for all r 0 if x spec i we also say that r is p regular thus regular schemes are ifn regular for every n in contrast it was observed as long ago as in 2 that a nonreduced affine scheme can never be k regular in particular if a is an artinian ring that is a o dimensional noetherian ring then a is regular that is reduced if and only if a is ifi regular in 17 vorst conjectured that for an affine scheme x of finite type over a field f and of dimension d regularity and k i regularity are equivalent vorst proved this conjecture for d 1 by proving that regularity implies normality in this paper we prove vorst s conjecture in all dimensions provided the char acteristic of the ground field f is zero in fact we prove a stronger statement we say that x is regular in codimension n in x note that for all n z if a ring r is ifn regular then it is kn i regular this is proved in 17 for n 1 and in 6 4 4 for n kh x where k x is the algebraic if theory spectrum of x and kh x is the homotopy if theory of x defined in 19 we write fk r for fk spec r theorem 0 1 let r be a commutative ring which is essentially of finite type over a field f of characteristic 0 then the following hold a if tk r is n connected then r is regular in codimension khi x is an isomorphism for i n and a surjection for i n 1 so that fk x

group cohomology and the cyclic cohomology of crossed products definite results are obtained in the conditions the group g is torsion free and the class h of the extension 0 zh g h n h 0 in h2 nh k is niipotent here gh for h g stands for the centralizer of h the cyclic homology groups hc a g decompose naturally as a direct sum of two subgroups called the homogeneous and the inhomogeneous parts ofhc a g the homogeneous part can be obtained from a spectral sequence converging to it with e2 q hp g hcq a the inhomogeneous part vanishes after inverting s for g z and in the topological situation we thus reobtain the result of nest 17 for general g but a k and trivial action thus for group rings k g we reobtain results of burghelea 4 the free groups satisfy our conditions see 10 for other classes of groups satisfying these conditions in this case our results are compatible with the results of pimsner and voiculescu 18 19 and suggest that for a large class of groups the part of ktor a r d g is obtained from a convergent spectral sequence with e q hp g k here r176 denotes the topological k theory functors see 2 a is a c algebra and a d g the reduced crossed product c algebra is a suitable completion of a g kasparov 13 succeeded to prove this for groups having a special manifold as classifying space we expect that our spectral sequence will give more insight in kasparov s spectral sequence we also mention

bicomplex formulation and moyal deformation of 2 1 dimensional fordy kulish systems using bicomplex formalism we construct generalizations of fordy kulish systems of matrix nonlinear schrodinger equations on two dimensional space time in two respects firstly we obtain corresponding equations in three space time dimensions secondly a moyal deformation is applied to the space time coordinates and the ordinary product of functions replaced by the moyal product in a suitable way both generalizations preserve the existence of an infinite set of conservation laws

extended super kac moody algebras and their super derivation algebras we study then extended super kac moody algebras i e extensions of the lie algebra of the loop group over the super circlea n the extensions are characterized by 2 cocycles which are computed in terms of the cyclic cohomology of the grassmann algebra withn generators the graded algebra of super derivations compatible with each extension is determined the casesn 1 2 3 are examined in detail and their relation with the ademollo et al superconformal algebras is discussed we examine the possibility of defining new superconformal algebras which forn 1 generalize then 1 ramond neveu schwarz algebra

two dimensional exactly and completely integrable dynamical systems monopoles instantons dual models relativistic strings lund regge model generalized toda lattice etc an investigation of two dimensional exactly and completely integrable dynamical systems associated with the local part of an arbitrary lie algebra mathfrak g whose grading is consistent with an arbitrary integral embedding of 3d subalgebra in mathfrak g has been carried out we have constructed in an explicit form the corresponding systems of nonlinear partial differential equations of the second order and obtained their general solutions in the sense of a goursat problem a method for the construction of a wide class of infinite dimensional lie algebras of finite growth has been proposed

weighted quasi equilibrium problems with lower and upper bounds abstract this paper is devoted to studying the solution existence of weighted quasi equilibrium problems with lower and upper bounds by using maximal element theorems a fixed point theorem of set valued mappings and fan kkm theorem respectively some new results are obtained

hochschild and cyclic homology of yang mills algebras the aim of this article is to compute the hochschild and cyclic homology groups of the yang mills algebras ym n n n 2 defined by a connes and m dubois violette in cd1 contin uing thus the study of these algebras that we have initiated in hs the computation involves the use of a spectral sequence associated to the natural filtration on the universal enveloping algebra ym n provided by a lie idealtym n inym n which is free as lie algebra 2000 mathematics subject classification 16e40 16s32 17b56 70s15 81t13