Twisted actions and regular Fell bundles over inverse semigroups

Abstract

We introduce a new notion of twisted actions of inverse semigroups and show that they correspond bijectively to certain regular Fell bundles over inverse semigroups, yielding in this way a structure classification of such bundles. These include as special cases all the stable Fell bundles. Our definition of twisted actions properly generalizes a previous one introduced by Sieben and corresponds to Busby-Smith twisted actions in the group case. As an application we describe twisted etale groupoid C*-algebras in terms of crossed products by twisted actions of inverse semigroups and show that Sieben's twisted actions essentially correspond to twisted etale groupoids with topologically trivial twists.

35 pages

References in corpus (2)

• Fell bundles over inverse semigroups and twisted etale groupoids
• C*-Crossed Products by Twisted Inverse Semigroup Actions

Cited by in corpus (10)

• Inverse semigroup actions on groupoids
• Stone duality and quasi-orbit spaces for generalised C*-inclusions
• Amenability and approximation properties for partial actions and Fell bundles
• Quantales and Fell bundles
• Inverse semigroup expansions and their actions on C*-algebras
• Banach algebras associated to twisted étale groupoids: inverse semigroup disintegration and representations on $L^p$-spaces
• $\mathrm{K}$-theory and homotopies of twists on ample groupoids
• On Fell bundles over inverse semigroups and their left regular representations
• On Cohomology for Product Systems
• Partial cohomology of groups and extensions of semilattices of abelian groups