Twisted actions and regular Fell bundles over inverse semigroups

Details Twisted actions and regular Fell bundles over inverse semigroups Twisted actions and regular Fell bundles over inverse semigroups

2010-03-02

arxiv.org/abs/1003.0613v1

Mathematics

Operator Algebras

35 pages

Scientific paper

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.

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