Renault's Equivalence Theorem for Reduced Groupoid C*-algebras

2010/02/16 by Aidan Sims, Sims, Aidan, Dana P. Williams +1 · 1 citation
Mathematics · #46L55 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Homotopy and Cohomology in Algebraic Topology #Operator Algebras (math.OA) #math.FA #math.OA #msc:46L55

paper · pdf · doi:10.48550/arxiv.1002.3093

14 Pages, added references with minor changes to the introduction and the end of section one

openalex publication_date 2010/02/16 · arxiv created 2010/07/13 · arxiv updated 2010/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We use the technology of linking groupoids to show that equivalent groupoids have Morita equivalent reduced C*-algebras. This equivalence is compatible in a natural way in with the Equivalence Theorem for full groupoid C*-algebras.

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• Some remarks about the weak containment property for groupoids and semigroups

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