Simplicity of C*-algebras associated to higher-rank graphs

DOI10.1112/blms/bdm006zbMath1125.46045arXivmath/0602120OpenAlexW2134707718MaRDI QIDQ5297620

Aidan Sims, David Robertson

Publication date: 12 July 2007

Published in: Bulletin of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0602120

Mathematics Subject Classification ID

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

Related Items (41)

AF-embeddability of 2-graph algebras and quasidiagonality of \(k\)-graph algebras ⋮ CO-UNIVERSAL C*-ALGEBRAS ASSOCIATED TO APERIODIC k-GRAPHS ⋮ Homotopy of product systems and K-theory of Cuntz-Nica-Pimsner algebras ⋮ Higher dimensional generalizations of the Thompson groups ⋮ PERIODIC -GRAPH ALGEBRAS REVISITED ⋮ Kumjian-Pask algebras of locally convex higher-rank graphs. ⋮ Separable representations, KMS states, and wavelets for higher-rank graphs ⋮ \(K\)-theory for real \(k\)-graph \(C^\ast\)-algebras ⋮ Purely infinite simple Kumjian-Pask algebras ⋮ Uniqueness theorems for topological higher-rank graph 𝐶*-algebras ⋮ Some results regarding the ideal structure of C∗$C^*$‐algebras of étale groupoids ⋮ Irreducibility and monicity for representations of \(k\)-graph \(C^*\)-algebras ⋮ Deformations of Fell bundles and twisted graph algebras ⋮ \(C^{\star}\)-algebras of higher-rank graphs from groups acting on buildings, and explicit computation of their \(K\)-theory ⋮ Zappa-Szép products of semigroups and their \(C^\ast\)-algebras ⋮ Skew-products of higher-rank graphs and crossed products by semigroups ⋮ A generalized Cuntz-Krieger uniqueness theorem for higher-rank graphs ⋮ Spectral triples for higher-rank graph $C^*$-algebras ⋮ KMS states of self-similar \(k\)-graph \(C^*\)-algebras ⋮ Cohn path algebras of higher-rank graphs ⋮ Simplicity of algebras associated to étale groupoids ⋮ Aperiodicity and primitive ideals of row-finite k-graphs ⋮ Two families of Exel-Larsen crossed products ⋮ Centers of algebras associated to higher-rank graphs. ⋮ PERIODIC 2-GRAPHS ARISING FROM SUBSHIFTS ⋮ Remarks on some fundamental results about higher-rank graphs and their C*-algebras ⋮ Spectral triples and wavelets for higher-rank graphs ⋮ KMS states on the \(C^\ast\)-algebra of a higher-rank graph and periodicity in the path space ⋮ Aperiodicity and cofinality for finitely aligned higher-rank graphs ⋮ Purely infinite -algebras associated to étale groupoids ⋮ Cohomology for small categories: \(k\)-graphs and groupoids ⋮ Simplicity of \(C^*\)-algebras associated to row-finite locally convex higher-rank graphs ⋮ Cycline subalgebras of 𝑘-graph C*-algebras ⋮ Symmetries of the KMS simplex ⋮ Simplicity of twisted \(C^\ast\)-algebras of higher-rank graphs and crossed products by quasifree actions ⋮ COVERINGS OF SKEW-PRODUCTS AND CROSSED PRODUCTS BY COACTIONS ⋮ A family of 2-graphs arising from two-dimensional subshifts ⋮ Generalized gauge actions on $\kappa$-graph $C*-Algebras: KMS states and Hausdorff structure ⋮ Isomorphism of the cubical and categorical cohomology groups of a higher-rank graph ⋮ Kumjian-Pask algebras of higher-rank graphs ⋮ On twisted higher-rank graph 𝐶*-algebras

Cites Work

• Graphs, groupoids, and Cuntz-Krieger algebras
• Cuntz-Krieger algebras of directed graphs
• The \(C^*\)-algebras of row-finite graphs
• The \(C^*\)-algebras of finitely aligned higher-rank graphs
• Higher rank graph \(C^*\)-algebras
• The \(C^*\)-algebras of arbitrary graphs
• Affine buildings, tiling systems and higher rank Cuntz-Krieger algebras
• HIGHER-RANK GRAPHS AND THEIR $C^*$-ALGEBRAS
• The 𝐶*-algebras of infinite graphs

This page was built for publication: Simplicity of C*-algebras associated to higher-rank graphs