Journal of Operator Theory

Volume 67, Issue 1, Winter 2012 pp. 153-205.

Fell bundles over inverse semigroups and twisted etale groupoids

Authors: Alcides Buss (1) and Ruy Exel (2)
Author institution: (1) Departamento de Matematica, Universidade Federal de Santa Catarina, 88.040-900 Florianopolis-SC, Brasil
(2) Departamento de Matematica, Universidade Federal de Santa Catarina, 88.040-900 Florianopolis-SC, Brasil

Summary: 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

$(\G,\Sigma)$ such that

$\A$ can be recovered from

$(\G,\Sigma)$ 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.

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