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2017 Inverse semigroup actions on groupoids
Alcides Buss, Ralf Meyer
Rocky Mountain J. Math. 47(1): 53-159 (2017). DOI: 10.1216/RMJ-2017-47-1-53

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 \'etale groupoids. We interpret these as actions on $C^*$\nobreakdash -algebras by Hilbert bimodules and describe the section algebras of these Fell bundles.

Our constructions give saturated Fell bundles over non-Hausdorff \'etale 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 stabilization trick does not generalize to non-Hausdorff groupoids.

Citation

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Alcides Buss. Ralf Meyer. "Inverse semigroup actions on groupoids." Rocky Mountain J. Math. 47 (1) 53 - 159, 2017. https://doi.org/10.1216/RMJ-2017-47-1-53

Information

Published: 2017
First available in Project Euclid: 3 March 2017

zbMATH: 06702339
MathSciNet: MR3619758
Digital Object Identifier: 10.1216/RMJ-2017-47-1-53

Subjects:
Primary: 20M18, 22A22, 46L55

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

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Vol.47 • No. 1 • 2017
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