Fell bundles over inverse semigroups and twisted etale groupoids

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.

43 pages; revised version with substantial changes in the text and references; To appear in "Journal of Operator Theory"

References in corpus (4)

• Renault's Equivalence Theorem for Groupoid Crossed Products
• Noncommutative Cartan sub-algebras of C*-algebras
• Non-Hausdorff groupoids
• Tight representations of semilattices and inverse semigroups

Cited by in corpus (13)

• Twisted actions and regular Fell bundles over inverse semigroups
• Aperiodicity: the almost extension property and uniqueness of pseudo-expectations
• Essential crossed products for inverse semigroup actions: simplicity and pure infiniteness
• Stone duality and quasi-orbit spaces for generalised C*-inclusions
• Iterated crossed products for groupoid fibrations
• A universal property for groupoid C*-algebras. I
• Quantales and Fell bundles
• Zappa-Szép product of a Fell bundle and a groupoid
• Linear structures on locales
• Representations of *-algebras by unbounded operators: C*-hulls, local-global principle, and induction
• Equivalence of Fell bundles is an equivalence relation
• On Fell bundles over inverse semigroups and their left regular representations
• Localised Hilbert modules and weak noncommutative Cartan pairs