## Rocky Mountain Journal of Mathematics

### 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 \'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.

#### Article information

Source
Rocky Mountain J. Math., Volume 47, Number 1 (2017), 53-159.

Dates
First available in Project Euclid: 3 March 2017

https://projecteuclid.org/euclid.rmjm/1488531894

Digital Object Identifier
doi:10.1216/RMJ-2017-47-1-53

Mathematical Reviews number (MathSciNet)
MR3619758

Zentralblatt MATH identifier
06702339

#### Citation

Buss, Alcides; Meyer, Ralf. Inverse semigroup actions on groupoids. Rocky Mountain J. Math. 47 (2017), no. 1, 53--159. doi:10.1216/RMJ-2017-47-1-53. https://projecteuclid.org/euclid.rmjm/1488531894

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