Simplicity of twisted \(C^\ast\)-algebras of higher-rank graphs and crossed products by quasifree actions

DOI10.4171/JNCG/241zbMath1362.46053arXiv1411.3860OpenAlexW2962801239MaRDI QIDQ740101

Aidan Sims, David Pask, Alexander Kumjian

Publication date: 12 August 2016

Published in: Journal of Noncommutative Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.3860

zbMATH Keywords

cohomologygroupoidcocyclecrossed productgraph algebra\(C^\ast\)-algebrasimplicity\(k\)-graphquasifree actiontwisted \(C^\ast\)-algebra

Mathematics Subject Classification ID

Noncommutative dynamical systems (46L55) General theory of (C^*)-algebras (46L05)

Related Items (8)

\(C^\ast\)-algebras of extensions of groupoids by group bundles ⋮ The primitive ideals of some étale groupoid \(C^\ast\)-algebras ⋮ A uniqueness theorem for twisted groupoid \(C^{*}\)-algebras ⋮ SIMPLICITY OF TWISTED C*-ALGEBRAS OF TOPOLOGICAL HIGHER-RANK GRAPHS ⋮ Simplicity of twisted C*-algebras of Deaconu-Renault groupoids ⋮ Twisted Steinberg algebras ⋮ Product-system models for twisted \(C^{\ast}\)-algebras of topological higher-rank graphs ⋮ KMS states on theC*-algebras of Fell bundles over groupoids

Cites Work

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• Crossed products and twisted \(k\)-graph algebras
• The primitive ideals of some étale groupoid \(C^\ast\)-algebras
• Amenability for Fell bundles over groupoids
• Homology for higher-rank graphs and twisted \(C^*\)-algebras
• Twisted \(C^*\)-algebras associated to finitely aligned higher-rank graphs
• Noncommutative manifolds from graph and \(k\)-graph \(C^*\)-algebras
• \(K\)-theory and homotopies of 2-cocycles on higher-rank graphs
• Higher-rank graph \(C^*\)-algebras: an inverse semigroup and groupoid approach
• Cuntz-Krieger algebras of directed graphs
• A groupoid approach to C*-algebras
• Outer automorphisms and reduced crossed products of simple C*-algebras
• Induced representations and Banach \(^*\)-algebraic bundles. With an appendix due to A. Douady and L. Dal Soglio-Herault
• Fundamental groupoids of \(k\)-graphs
• Multiplier representations of Abelian groups
• On the \(K\)-theory of twisted higher-rank-graph \(C^{\ast }\)-algebras
• A classification theorem for nuclear purely infinite simple \(C^*\)-algebras
• Twisted \(k\)-graph algebras associated to Bratteli diagrams
• Simplicity of algebras associated to étale groupoids
• UCT-Kirchberg algebras have nuclear dimension one
• The primitive ideals of the Cuntz-Krieger algebra of a row-finite higher-rank graph with no sources
• A generalized Cuntz-Krieger uniqueness theorem for higher-rank graphs
• On the \(K\)-theory of higher rank graph \(C^*\)-algebras
• Multipliers on Abelian groups
• Groupoids and $C^*$-algebras for categories of paths
• The noncommutative geometry of k-graph C*-algebras
• Aperiodicity and cofinality for finitely aligned higher-rank graphs
• Cartan subalgebras in C*-algebras
• Periodicity in Rank 2 Graph Algebras
• Twisted crossed products of C*-algebras
• Affine buildings, tiling systems and higher rank Cuntz-Krieger algebras
• Purely infinite $C^*$-algebras arising from dynamical systems
• Fell bundles over groupoids
• Remarks on the Ideal Structure of Fell Bundle C*-Algebras
• Remarks on some fundamental results about higher-rank graphs and their C*-algebras
• On twisted higher-rank graph 𝐶*-algebras
• Simplicity of C*-algebras associated to higher-rank graphs

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