Fell bundles over groupoids

TL;DR

This paper explores Fell bundles over groupoids, providing foundational definitions, structural insights, and a Morita equivalence theorem that generalizes semi-direct products of groups with C^*-algebras.

Contribution

It introduces new structural results and a Morita equivalence theorem for Fell bundles over topological groupoids, expanding the theoretical framework.

Findings

Established a Morita equivalence theorem for Fell bundles

Generalized semi-direct products of groups with C^*-algebras

Provided foundational definitions and structural results

Abstract

The author provides some definitions and structural results about Fell bundles, defined as C^*-algebra bundles over topological groupoids. Such bundles are a mutual generalization of semi-direct products of groups with C^*-algebras and C^*-algebra bundles over topological spaces. In particular a Morita equivalence theorem with semi-direct products is established.