Renault's Equivalence Theorem for Groupoid Crossed Products

TL;DR

This paper explains Renault's equivalence theorem for groupoid crossed products, emphasizing the bundle approach and imprimitivity bimodules, serving as groundwork for the Brauer semigroup in this context.

Contribution

It offers a detailed exposition and proof of Renault's theorem focusing on the bundle approach and imprimitivity bimodules, advancing the understanding of groupoid crossed products.

Findings

Provides a comprehensive proof of Renault's equivalence theorem

Highlights the bundle approach and imprimitivity bimodules

Prepares for analysis of the Brauer semigroup in groupoid contexts

Abstract

We provide an exposition and proof of Renault's equivalence theorem for crossed products by locally Hausdorff, locally compact groupoids. Our approach stresses the bundle approach, concrete imprimitivity bimodules and is a preamble to a detailed treatment of the Brauer semigroup for a locally Hausdorff, locally compact groupoid.