Reconstructing a totally disconnected groupoid from its ample semigroup

2009/07/27 by Ruy Exel, Exel, Ruy · 2 citations
Mathematics · #20M18 #20M30 #22A22 #46L55 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Dynamical Systems (math.DS) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Operator Algebras (math.OA) #math.DS #math.OA #msc:20M18 #msc:20M30 #msc:22A22 #msc:46L55

paper · pdf · doi:10.48550/arxiv.0907.4530

10 pages

arxiv created 2009/07/27 · openalex publication_date 2009/07/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that a (not necessarily Hausdorff) etale, second countable groupoid G with totally disconnected unit space may be reconstructed solely from the algebraic structure of its ample semigroup S. We also show that C*(G) possesses a universal property related to tight representations of S.

Cited by

• Graded Lawson-Stone Duality
• Rigidity of pseudofunction algebras of ample groupoids

Related

• Reconstructing Etale Groupoids from Semigroups
• Simplicity of inverse semigroup and étale groupoid algebras
• Simplicity of algebras associated to étale groupoids
• A non-amenable groupoid whose maximal and reduced C^*-algebras are the same
• A dichotomy for groupoid C*-algebras