Fell bundles and imprimitivity theorems

TL;DR

This paper applies the Yamagami-Muhly-Williams equivalence theorem for Fell bundles over groupoids to recover and extend imprimitivity theorems involving groups, including a symmetric version and new theoretical tools.

Contribution

It extends Raeburn's symmetric imprimitivity theorem and develops new tools for Fell bundle theory not previously documented.

Findings

Extended Raeburn's symmetric imprimitivity theorem

Developed new tools for Fell bundle theory

Unified approach to imprimitivity theorems

Abstract

Our goal in this paper and two sequels is to apply the Yamagami-Muhly-Williams equivalence theorem for Fell bundles over groupoids to recover and extend all known imprimitivity theorems involving groups. Here we extend Raeburn's symmetric imprimitivity theorem, and also, in an appendix, we develop a number of tools for the theory of Fell bundles that have not previously appeared in the literature.