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arXiv · 1410.2051

Inverse semigroup actions on groupoids

Alcides Buss·Ralf Meyer
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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.

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Alcides Buss, Ralf Meyer. 2017-01-09. Inverse semigroup actions on groupoids. https://doi.org/10.1216/rmj-2017-47-1-53

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