Fell bundles over inverse semigroups and twisted etale groupoids

2009/03/19 by Alcides Buss, Buss, Alcides, Ruy Exel +1 · 2 citations
Mathematics · #20M18 #46L45 #46L55 #55R65 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Geometric and Algebraic Topology #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.0903.3388

openalex publication_date 2009/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a saturated Fell bundle A over an inverse semigroup S which is semi-abelian in the sense that the fibers over the idempotents of S are commutative, we construct a twisted etale groupoid L such that A can be recovered from L in a canonical way. As an application we recover most of Renault's recent result on the classification of Cartan subalgebras of C*-algebras through twisted etale groupoids.

Citations

• Noncommutative Cartan sub-algebras of C*-algebras

Cited by

• Spectral sequence computation of higher twisted 𝐾-groups of 𝑆𝑈(𝑛)
• The action of an inverse semigroup on its Stone-Čech compactification

Related

• Cartan semigroups and twisted groupoid C*-algebras
• C^*-algebras of Fell bundles over étale groupoids
• Fell bundles associated to groupoid morphisms
• Twists, crossed products and inverse semigroup cohomology
• Representing Structured Semigroups on Etale Groupoid Bundles