Inverse semigroup actions on groupoids
Inverse semigroup actions on groupoids
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 …