共查询到20条相似文献,搜索用时 15 毫秒
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Alex Kumjian 《Proceedings of the American Mathematical Society》1998,126(4):1115-1125
We study the C*-algebras associated to Fell bundles over groupoids and give a notion of equivalence for Fell bundles which guarantees that the associated C*-algebras are strongly Morita equivalent. As a corollary we show that any saturated Fell bundle is equivalent to a semi-direct product arising from the action of the groupoid on a C*-bundle.
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We prove that a number of classes of separable unital C*-algebras are closed under crossed products by finite group actions with the Rokhlin property, including: (a) AI algebras, AT algebras, and related classes characterized by direct limit decompositions using semiprojective building blocks. (b) Simple unital AH algebras with slow dimension growth and real rank zero. (c) C*-algebras with real rank zero or stable rank one. (d) Simple C*-algebras for which the order on projections is determined by traces. (e) C*-algebras whose quotients all satisfy the Universal Coefficient Theorem. (f) C*-algebras with a unique tracial state. Along the way, we give a systematic treatment of the derivation of direct limit decompositions from local approximation conditions by homomorphic images which are not necessarily injective. 相似文献
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To an inverse semigroup, we associate an étale groupoid such that its actions on topological spaces are equivalent to actions of the inverse semigroup. Both the object and the arrow space of this groupoid are non-Hausdorff. We show that this construction provides an adjoint functor to the functor that maps a groupoid to its inverse semigroup of bisections, where we turn étale groupoids into a category using algebraic morphisms. We also discuss how to recover a groupoid from this inverse semigroup. 相似文献
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Bertrand Monthubert 《Journal of Functional Analysis》2003,199(1):243-286
We associate to any manifold with corners (even with non-embedded hyperfaces) a (non-Hausdorff) longitudinally smooth Lie groupoid, on which we define a pseudodifferential calculus. This calculus generalizes the b-calculus of Melrose, defined for manifolds with embedded corners. The groupoid of a manifold with corners is shown to be unique up to equivalence for manifolds with corners of same codimension. Using tools from the theory of C∗-algebras of groupoids, we also obtain new proofs for the study of b-calculus. 相似文献
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The theory of crossed products of C~*-algebras by groups of automorphisms is a well-developed area of the theory of operator algebras. Given the importance and the success ofthat theory, it is natural to attempt to extend it to a more general situation by, for example,developing a theory of crossed products of C~*-algebras by semigroups of automorphisms, or evenof endomorphisms. Indeed, in recent years a number of papers have appeared that are concernedwith such non-classical theories of covariance algebras, see, for instance [1-3]. 相似文献
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Emmanuel Breuillard Mehrdad Kalantar Matthew Kennedy Narutaka Ozawa 《Publications Mathématiques de L'IHéS》2017,126(1):35-71
A discrete group is said to be C*-simple if its reduced C*-algebra is simple, and is said to have the unique trace property if its reduced C*-algebra has a unique tracial state. A dynamical characterization of C*-simplicity was recently obtained by the second and third named authors. In this paper, we introduce new methods for working with group and crossed product C*-algebras that allow us to take the study of C*-simplicity a step further, and in addition to settle the longstanding open problem of characterizing groups with the unique trace property. We give a new and self-contained proof of the aforementioned characterization of C*-simplicity. This yields a new characterization of C*-simplicity in terms of the weak containment of quasi-regular representations. We introduce a convenient algebraic condition that implies C*-simplicity, and show that this condition is satisfied by a vast class of groups, encompassing virtually all previously known examples as well as many new ones. We also settle a question of Skandalis and de la Harpe on the simplicity of reduced crossed products. Finally, we introduce a new property for discrete groups that is closely related to C*-simplicity, and use it to prove a broad generalization of a theorem of Zimmer, originally conjectured by Connes and Sullivan, about amenable actions. 相似文献
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We define the notion of crossed modules for Lie 2-algebras. To a given crossed module, we associate a strict Lie 3-algebra structure on its mapping cone complex and a strict Lie 2-algebra structure on its derivations. Finally, we classify strong crossed modules by means of the third cohomology group of Lie 2-algebras. 相似文献
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This paper is concerned with the algebraic structure of groupoids and crossed modules of groupoids. We describe the group
structure of the automorphism group of a finite connected groupoid C as a quotient of a semidirect product. We pay particular attention to the conjugation automorphisms of C, and use these to define a new notion of groupoid action. We then show that the automorphism group of a crossed module of
groupoids C\mathcal{C}, in the case when the range groupoid is connected and the source group totally disconnected, may be determined from that
of the crossed module of groups Cu\mathcal{C}_u formed by restricting to a single object u. Finally, we show that the group of homotopies of C\mathcal{C} may be determined once the group of regular derivations of Cu\mathcal{C}_u is known. 相似文献
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In this article, we introduce the notions of restricted Lie 2-algebras and crossed modules of restricted Lie algebras, and give a series of examples of restricted Lie 2-algebras. We also construct restricted Lie 2-algebras from A(m)-algebras, restricted Leibniz algebras, restricted right-symmetric algebras. Finally, we prove that there is a one-to-one correspondence between strict restricted Lie 2-algebras and crossed modules of restricted Lie algebras. 相似文献
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Archiv der Mathematik - We prove a change of base theorem for operator space modules over C*-algebras, analogous to the change of rings for algebraic modules. We demonstrate how this can be used to... 相似文献
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We prove an analog of the Stinespring theorem for Hilbert modules over local C*-algebras. 相似文献
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Dijana Ilisevic Sanja Varosanec 《Proceedings of the American Mathematical Society》2005,133(11):3271-3280
In this paper we give some properties of a generalized inner product in modules over H*-algebras and C*-algebras and we obtain inequalities of Grüss type.
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证明了一类C~*-代数的弱无孔性质可以遗传到通过此类C~*-代数迹逼近后得到的C~*-代数中.同时证明了具有弱无孔性质的C~*-代数经过具有迹Rokhlin性质的有限群作用后得到的交叉积C~*-代数也具有弱无孔性质。 相似文献
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We analyze the decomposition rank (a notion of covering dimensionfor nuclear C*-algebras introduced by E. Kirchberg and the author)of subhomogeneous C*-algebras. In particular, we show that asubhomogeneous C*-algebra has decomposition rank n if and onlyif it is recursive subhomogeneous of topological dimension n,and that n is determined by the primitive ideal space. As an application, we use recent results of Q. Lin and N. C.Phillips to show the following. Let A be the crossed productC*-algebra coming from a compact smooth manifold and a minimaldiffeomorphism. Then the decomposition rank of A is dominatedby the covering dimension of the underlying manifold. 2000 MathematicsSubject Classification 46L85, 46L35. 相似文献
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We define what it means for a proper continuous morphism between groupoids to be Haar system preserving, and show that such a morphism induces (via pullback) a *-morphism between the corresponding convolution algebras. We proceed to provide a plethora of examples of Haar system preserving morphisms and discuss connections to noncommutative CW-complexes and interval algebras. We prove that an inverse system of groupoids with Haar system preserving bonding maps has a limit, and that we get a corresponding direct system of groupoid -algebras. An explicit construction of an inverse system of groupoids is used to approximate a σ-compact groupoid G by second countable groupoids; if G is equipped with a Haar system and 2-cocycle then so are the approximation groupoids, and the maps in the inverse system are Haar system preserving. As an application of this construction, we show how to easily extend the Maximal Equivalence Theorem of Jean Renault to σ-compact groupoids. 相似文献
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具拟不变测度群胚流上的交叉积 总被引:2,自引:0,他引:2
设G为第二可数局部紧有Haar系{λu}的群胚,A为G上左不变作用的交换群,则我们有C-动力系统(C(G),A,β).本文我们研究具有一定性质的拟不变测度,用此测度,得到了一些有关群胚C-代数及交叉积的重要结果, 相似文献