Groupoid and inverse semigroup presentations of ultragraph \(C^{*}\)-algebras

DOI10.1007/s00233-008-9046-8zbMath1185.46038arXiv0709.2281OpenAlexW2090457309MaRDI QIDQ1006329

Paul S. Muhly, Alberto E. Marrero

Publication date: 20 March 2009

Published in: Semigroup Forum (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0709.2281

zbMATH Keywords

representationsamenabilityinverse semigroupultragraph \(C^*\)-algebraCuntz-Krieger familyessentially principal groupoidultragraph groupoid

Mathematics Subject Classification ID

Noncommutative dynamical systems (46L55) General theory of (C^*)-algebras (46L05) Graph theory (05C99) Topological groupoids (including differentiable and Lie groupoids) (22A22) Inverse semigroups (20M18) Means on groups, semigroups, etc.; amenable groups (43A07) Representation of semigroups; actions of semigroups on sets (20M30)

Related Items

Inverse semigroups associated with labelled spaces and their tight spectra, KMS states and continuous orbit equivalence for ultragraph shift spaces with sinks, Uniqueness theorems for topological higher-rank graph 𝐶*-algebras, Realizing ultragraph Leavitt path algebras as Steinberg algebras, Groupoid models for the \(C^*\)-algebra of labelled spaces, Monopoles, dipoles, and harmonic functions on Bratteli diagrams, Li-Yorke chaos for ultragraph shift spaces, \(C^\ast\)-algebras associated to Boolean dynamical systems, KMS and ground states on ultragraph \( C^*\)-algebras, Continuous shift commuting maps between ultragraph shift spaces, Ultragraph algebras via labelled graph groupoids, with applications to generalized uniqueness theorems, 𝑊-Markov measures, transfer operators, wavelets and multiresolutions, Ultragraph shift spaces and chaos, A groupoid approach to discrete inverse semigroup algebras, A Conditional Expectation on the Tensor Product of Exel-Laca algebras

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