Noncommutative boundaries and the ideal structure of reduced crossed products

DOI10.1215/00127094-2019-0032OpenAlexW2761648792MaRDI QIDQ2286325

Matthew Kennedy, Christopher P. Schafhauser

Publication date: 22 January 2020

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.02200

zbMATH Keywords

ideal structure\(C^*\)-dynamical systemreduced crossed productnoncommutative boundary

Mathematics Subject Classification ID

Noncommutative dynamical systems (46L55) Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis) (43A65) Classifications of (C^*)-algebras (46L35) Crossed product algebras (analytic crossed products) (47L65)

Related Items (16)

Noncommutative Choquet simplices ⋮ A generalized Powers averaging property for commutative crossed products ⋮ Amenability, proximality and higher-order syndeticity ⋮ Essential crossed products for inverse semigroup actions: simplicity and pure infiniteness ⋮ Furstenberg boundary of minimal actions ⋮ Boundary maps and covariant representations ⋮ Regular ideals, ideal intersections, and quotients ⋮ Partial generalized crossed products and a seven term exact sequence ⋮ The third partial cohomology group and existence of extensions of semilattices of groups by groups ⋮ Partial generalized crossed products and a seven-term exact sequence ⋮ Characterizing traces on crossed products of noncommutative \(\mathrm{C}^\ast\)-algebras ⋮ Unique expectations for discrete crossed products ⋮ Recent developments around partial actions ⋮ Globalization of group cohomology in the sense of Alvares-Alves-Redondo ⋮ Boundary maps, germs and quasi-regular representations ⋮ Schur's theory for partial projective representations

Cites Work

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• Unique pseudo-expectations for \(C^{*}\)-inclusions
• Unique conditional expectations for abelian \(C^\ast\)-inclusions
• \(C^*\)-simplicity and the unique trace property for discrete groups
• Properties of topological dynamical systems and corresponding \(C^*\)- algebras
• Projective topological spaces
• Injective envelopes of \(C^*\)-dynamical systems
• Injective envelopes of operator systems
• Some simple C*-algebras constructed as crossed products with discrete outer automorphism groups
• Regular embeddings of C*-algebras in monotone complete C*-algebras
• Proximal flows
• Unique expectations for discrete crossed products
• Applications of the Connes spectrum to C*-dynamical systems. III
• Partial cohomology of groups.
• Boundaries of reduced \(C^\ast\)-algebras of discrete groups
• A generalization of free action
• Subalgebras of \(C^ *\)-algebras
• Uniformly recurrent subgroups
• A Hausdorff Topology for the Closed Subsets of a Locally Compact Non-Hausdorff Space
• Quasi-standard C*-algebras
• An intrinsic characterization of C*-simplicity
• A Correction to “A Structure Theory in the Regular σ-Completion of C^∗ -Algebras”
• The Krein-Milman theorem in operator convexity
• Topologically free actions and ideals in discrete C*-dynamical systems
• On the central Haagerup tensor product
• Partial Dynamical Systems, Fell Bundles and Applications
• The ideal structure of reduced crossed products
• Reduced Twisted Crossed Products over C*-Simple Groups
• Aperiodicity, topological freeness and pure outerness: from group actions to Fell bundles
• Structure for Regular Inclusions
• Topologies for Primal Ideals
• The Centre of the Regular Monotone Completion of a C^∗ -Algebra
• Injective envelopes and the intersection property
• Boundedness Properties in Function-Lattices
• A representation theory for commutative topological algebra
• Theory of operator algebras I.

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