Fell bundles over inverse semigroups and twisted etale groupoids
arXiv:0903.3388
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"