Twisted actions and regular Fell bundles over inverse semigroups
Operator Algebras
2014-02-26 v1
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.
Cite
@article{arxiv.1003.0613,
title = {Twisted actions and regular Fell bundles over inverse semigroups},
author = {Alcides Buss and Ruy Exel},
journal= {arXiv preprint arXiv:1003.0613},
year = {2014}
}
Comments
35 pages