Groupoid models of \(C^*\)-algebras and the Gelfand functor

zbMath1481.46048arXiv1804.00967MaRDI QIDQ2045868

Kyle Austin, Atish J. Mitra

Publication date: 16 August 2021

Published in: The New York Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.00967

zbMATH Keywords

Jiang-Su algebraGelfand functorgroupoid modelsRazak-Jacelon algebra

Mathematics Subject Classification ID

(C^*)-algebras and (W^*)-algebras in relation to group representations (22D25) General theory of (C^*)-algebras (46L05) Topological groupoids (including differentiable and Lie groupoids) (22A22)

Related Items (2)

A groupoid approach to interacting fermions ⋮ Classifiable \(\mathrm{C}^*\)-algebras from minimal \(\mathbb{Z} \)-actions and their orbit-breaking subalgebras

Cites Work

• Unnamed Item
• Unnamed Item
• Dynamic asymptotic dimension: relation to dynamics, topology, coarse geometry, and \(C^\ast\)-algebras
• Free loci of matrix pencils and domains of noncommutative rational functions
• Self-similar graphs, a unified treatment of Katsura and Nekrashevych \(C^\ast\)-algebras
• A groupoid approach to C*-algebras
• Reduction of topological stable rank in inductive limits of \(C^*\)- algebras
• The Baum-Connes conjecture for amenable foliations
• Inverse systems of groupoids, with applications to groupoid \(C^{\ast}\)-algebras
• Constructing minimal homeomorphisms on point-like spaces and a dynamical presentation of the Jiang-Su algebra
• Some classifiable groupoid \(C^{*}\)-algebras with prescribed \(K\)-theory
• Valuation methods in group rings and in skew fields. I
• Cartan subalgebras and the UCT problem
• Opposite algebras of groupoid \(C^*\)-algebras
• Cartan subalgebras and the UCT problem. II
• Every classifiable simple C\(^*\)-algebra has a Cartan subalgebra
• Topological construction of $C^*$-correspondences for groupoid $C^*$-algebras
• Renault's Equivalence Theorem for Reduced Groupoid C*-algebras
• The Jiang–Su algebra revisited
• Cartan subalgebras in C*-algebras
• On C*-Diagonals
• On a Simple Unital Projectionless C*-Algebra
• Inductive Limits of Interval Algebras: The Tracial State Space
• Groupoids Associated with Endomorphisms
• A simple, monotracial, stably projectionless C *‐algebra
• Rokhlin dimension for actions of residually finite groups
• Deformations of wreath products
• Groupoids as Coefficients
• 𝐴𝐹-algebras and the tail-equivalence relation on Bratteli diagrams

This page was built for publication: Groupoid models of \(C^*\)-algebras and the Gelfand functor