Inverse semigroup actions on groupoids
Abstract
We define inverse semigroup actions on topological groupoids by partial equivalences. From such actions, we construct saturated Fell bundles over inverse semigroups and non-Hausdorff étale groupoids. We interpret these as actions on C*-algebras by Hilbert bimodules and describe the section algebras of these Fell bundles. Our constructions give saturated Fell bundles over non-Hausdorff étale groupoids that model actions on locally Hausdorff spaces. We show that these Fell bundles are usually not Morita equivalent to an action by automorphisms. That is, the Packer-Raeburn Stabilisation Trick does not generalise to non-Hausdorff groupoids.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2014
- DOI:
- 10.48550/arXiv.1410.2051
- arXiv:
- arXiv:1410.2051
- Bibcode:
- 2014arXiv1410.2051B
- Keywords:
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- Mathematics - Operator Algebras;
- 46L55;
- 20M18;
- 22A22
- E-Print:
- 59 pages. Proofreading with minor changes. Version accepted for publication at Rocky Mountain Journal