Product systems over right-angled Artin semigroups

DOI10.1090/S0002-9947-01-02911-7zbMath1017.20032OpenAlexW1567894031MaRDI QIDQ2781371

Neal J. Fowler, Aidan Sims

Publication date: 19 March 2002

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

Full work available at URL: https://doi.org/10.1090/s0002-9947-01-02911-7

zbMATH Keywords

graphsfree groupsgraph productsproduct systemsright-angled Artin semigroupstensor groupoids

Mathematics Subject Classification ID

Free semigroups, generators and relations, word problems (20M05) Braid groups; Artin groups (20F36) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Groupoids, semigroupoids, semigroups, groups (viewed as categories) (18B40)

Related Items (18)

Topological aperiodicity for product systems over semigroups of Ore type ⋮ The \(C^*\)-algebras of finitely aligned higher-rank graphs ⋮ -ALGEBRAS FROM GROUP REPRESENTATIONS ⋮ CO-UNIVERSAL C*-ALGEBRAS ASSOCIATED TO APERIODIC k-GRAPHS ⋮ Higher dimensional generalizations of the Thompson groups ⋮ Simple modules for Kumjian-Pask algebras ⋮ \(C^{\star}\)-algebras of higher-rank graphs from groups acting on buildings, and explicit computation of their \(K\)-theory ⋮ The interplay between \(k\)-graphs and the Yang-Baxter equation. ⋮ When is the Cuntz-Krieger algebra of a higher-rank graph approximately finite-dimensional? ⋮ Co-universal \(C^*\)-algebras associated to generalised graphs ⋮ The noncommutative geometry of k-graph C*-algebras ⋮ Boundary Quotient -algebras of Products of Odometers ⋮ On the -theory of -algebras arising from integral dynamics ⋮ KMS states on \(C^{\ast}\)-algebras associated to a family of \(\ast\)-commuting local homeomorphisms ⋮ Remarks on some fundamental results about higher-rank graphs and their C*-algebras ⋮ Topological realizations and fundamental groups of higher-rank graphs ⋮ Kumjian-Pask algebras of higher-rank graphs ⋮ OBSTRUCTIONS TO A GENERAL CHARACTERIZATION OF GRAPH CORRESPONDENCES

Cites Work

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• Discrete product systems of Hilbert bimodules.
• Discrete product systems and their \(C^*\)-algebras
• Discrete product systems and twisted crossed products by semigroups
• Tensor algebras over \(C^*\)-correspondences: Representations, dilations, and \(C^*\)-envelopes
• Algorithms and geometry for graph products of groups
• Higher rank graph \(C^*\)-algebras
• On the Toeplitz algebras of right-angled and finite-type Artin groups
• Continuous analogues of Fock space
• Affine buildings, tiling systems and higher rank Cuntz-Krieger algebras
• The Toeplitz algebra of a Hilbert bimodule

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