Aperiodicity and cofinality for finitely aligned higher-rank graphs

DOI10.1017/S0305004110000034zbMath1213.46047arXiv0905.0735MaRDI QIDQ3586284

Aidan Sims, Peter Lewin

Publication date: 6 September 2010

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0905.0735

zbMATH Keywords

\(C^*\)-algebraCuntz-Krieger uniqueness theoremaperiodichigher-rank graphsfinitely aligned

Mathematics Subject Classification ID

General theory of (C^*)-algebras (46L05)

Related Items (17)

AF-embeddability of 2-graph algebras and quasidiagonality of \(k\)-graph algebras ⋮ Self-similark-Graph C*-Algebras ⋮ Groupoids and $C^*$-algebras for categories of paths ⋮ CO-UNIVERSAL C*-ALGEBRAS ASSOCIATED TO APERIODIC k-GRAPHS ⋮ Higher dimensional generalizations of the Thompson groups ⋮ PERIODIC -GRAPH ALGEBRAS REVISITED ⋮ Purely infinite simple Kumjian-Pask algebras ⋮ Higher dimensional generalizations of the Thompson groups via higher rank graphs ⋮ When is the Cuntz-Krieger algebra of a higher-rank graph approximately finite-dimensional? ⋮ A Cuntz-Krieger uniqueness theorem for semigraph \(C^\ast\)-algebras ⋮ Cohn path algebras of higher-rank graphs ⋮ Kumjian-Pask algebras of finitely aligned higher-rank graphs ⋮ Remarks on some fundamental results about higher-rank graphs and their C*-algebras ⋮ Twisted \(k\)-graph algebras associated to Bratteli diagrams ⋮ Simplicity of twisted \(C^\ast\)-algebras of higher-rank graphs and crossed products by quasifree actions ⋮ Kumjian-Pask algebras of higher-rank graphs ⋮ On twisted higher-rank graph 𝐶*-algebras

Cites Work

• Graphs, groupoids, and Cuntz-Krieger algebras
• Simplicity of \(C^*\)-algebras associated to row-finite locally convex higher-rank graphs
• Higher-rank graph \(C^*\)-algebras: an inverse semigroup and groupoid approach
• The \(C^*\)-envelope of the tensor algebra of a directed graph
• Atomic representations of rank 2 graph algebras
• Inverse semigroups and combinatorial \(C^*\)-algebras
• Cuntz-Krieger algebras of directed graphs
• A class of C*-algebras and topological Markov chains
• The \(C^*\)-algebras of finitely aligned higher-rank graphs
• Coverings of \(k\)-graphs
• A locally trivial quantum Hopf fibration.
• Gauge-Invariant Ideals in theC*-Algebras of Finitely Aligned Higher-Rank Graphs
• HIGHER-RANK GRAPHS AND THEIR $C^*$-ALGEBRAS
• A class of \boldmath{$C^*$}-algebras generalizing both graph algebras and homeomorphism \boldmath{$C^*$}-algebras I, fundamental results
• The 𝐶*-algebras of infinite graphs
• Simplicity of C*-algebras associated to higher-rank graphs
• Interpolation in semigroupoid algebras
• Relative Cuntz-Krieger algebras of finitely aligned higher-rank graphs
• TOPOLOGICAL QUIVERS

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