Amenability and exactness for dynamical systems and their 𝐶*-algebras

DOI10.1090/S0002-9947-02-02978-1zbMath1035.46039arXivmath/0005014OpenAlexW1554472687MaRDI QIDQ3151225

Claire Anantharaman-Delaroche

Publication date: 7 October 2002

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0005014

zbMATH Keywords

groupoidcrossed producttransformation groupsemi-direct productC*-algebraamenablenuclearinner amenable

Mathematics Subject Classification ID

Noncommutative dynamical systems (46L55) General theory of (C^*)-algebras (46L05) Means on groups, semigroups, etc.; amenable groups (43A07)

Related Items

Purely infinite C^*-algebras arising from crossed products, Fourier theory and \(C^\ast\)-algebras, Index theory on the Miščenko bundle, \(K\)-homological finiteness and hyperbolic groups, Non-amenable tight squeezes by Kirchberg algebras, On some permanence properties of exact groupoids, \(K\)-theory of certain purely infinite crossed products, Boundary amenability of $Out(F_N)$, Constructions preserving Hilbert space uniform embeddability of discrete groups, The Novikov conjecture for linear groups, Topological Boundaries of Unitary Representations, Exotic crossed products and the Baum-Connes conjecture, Boundaries of reduced \(C^\ast\)-algebras of discrete groups, Rigidity for equivalence relations on homogeneous spaces, Amenable and inner amenable actions and approximation properties for crossed products by locally compact groups, On the operator homology of the Fourier algebra and its \(cb\)-multiplier completion, Amenable dynamical systems over locally compact groups, Simple equivariant \(\mathrm{C}^\ast\)-algebras whose full and reduced crossed products coincide, Negative definite functions for \(C^*\)-dynamical systems, Boundary maps and covariant representations, Deformation of algebras associated with group cocycles, Property A and uniform embedding for locally compact groups, Morita enveloping Fell bundles, Groups with Spanier-Whitehead duality, Amenable purely infinite actions on the non-compact Cantor set, Coronas for properly combable spaces, Inner amenability and approximation properties of locally compact quantum groups, Amenable actions of inverse semigroups, A new family of representations of virtually free groups, On $C^*$-algebras associated to actions of discrete subgroups of $\operatorname{SL}(2,\mathbb{R})$ on the punctured plane, Relative amenability, The Fourier–Stieltjes algebra of a $C^*$-dynamical system II, Homotopy invariance of higher signatures and $3$-manifold groups, Injectivity, crossed products, and amenable group actions, Sofic boundaries of groups and coarse geometry of sofic approximations, Isoperimetry of group actions., Furstenberg boundaries for pairs of groups, Non-commutative entropy computations for continuous fields and cross-products, On characterizations of amenable \(\mathrm{C}^*\)-dynamical systems and new examples, On Ozawa kernels, Exactness and SOAP of crossed products via Herz-Schur multipliers, Exactness of locally compact groups, Fourier series and twisted \(C^*\)-crossed products, The Fourier–Stieltjes algebra of a C*-dynamical system, A new look at crossed product correspondences and associated \(C^\ast\)-algebras, Entropy of automorphisms arising from dynamical systems through discrete groups with amen\-able actions, Relative property (T) for the subequivalence relations induced by the action of SL\(_2(\mathbb Z)\) on \(\mathbb T^2\), Crossed products of the Cantor set by free minimal actions of \(\mathbb Z^d\), Exactness versus \(C^*\)-exactness for certain non-discrete groups, Fixed-point algebras for weakly proper Fell bundles, Ozawa's class𝒮for locally compact groups and unique prime factorization of group von Neumann algebras, Rank-one actions, their \((C, F)\)-models and constructions with bounded parameters, Busemann points of infinite graphs, The maximal injective crossed product, Unicorn paths and hyperfiniteness for the mapping class group, Equivariant -absorption theorem for exact groups, Half-exactness of the Kasparov equivariant bifunctor for amenable actions, Hyperlinear and Sofic Groups: A Brief Guide, A weak expectation property for operator modules, injectivity and amenable actions, QDQ vs. UCT, Amenability and approximation properties for partial actions and Fell bundles, Slant products on the Higson-Roe exact sequence, Amenability and the Liouville property

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Systèmes dynamiques non commutatifs et moyennabilité. (Non commutative dynamical systems and amenability)
• A groupoid approach to C*-algebras
• Classification of injective factors. Cases \(\mathrm{II}_1\), \(\mathrm{II}_\infty\), \(\mathrm{III}_\lambda\), \(\lambda\neq 1\)
• On non-semisplit extensions, tensor products and exactness of group \(C^*\)-algebras
• Boundary amenability for word hyperbolic groups and an application to smooth dynamics of simple groups
• Bivariant \(K\)-theory and the Novikov conjecture
• The coarse Baum-Connes conjecture and groupoids
• Exact groups and continuous bundles of \(C^*\)-algebras
• Amenable correspondences and approximation properties for von Neumann algebras
• The coarse Baum-Connes conjecture for spaces which admit a uniform embedding into Hilbert space
• On nuclear C\(^*\)-algebras
• Conjugation-invariant means
• Property Γ and Inner Amenability
• The completely bounded approximation property for discrete crossed products
• Approximation Properties for Group C∗-Algebras and Group Von Neumann Algebras
• Amenability for Fell bundles.
• Amenable actions and exactness for discrete groups
• Approximation property of C*-algebraic bundles
• Amenable group actions and the Novikov conjecture
• Inner Amenable Locally Compact Groups
• Exactness and the Novikov conjecture