Full and reduced coactions of locally compact groups on C*-algebras

TL;DR

This paper reviews the theory of full and reduced coactions of locally compact groups on C*-algebras, providing accessible explanations, new applications, and a novel version of Mansfield's imprimitivity theorem.

Contribution

It introduces a new version of Mansfield's imprimitivity theorem for full coactions and demonstrates its natural isomorphism between crossed-product functors.

Findings

New version of Mansfield's imprimitivity theorem

Establishment of natural isomorphism between crossed-product functors

Accessible survey with detailed explanations

Abstract

We survey the results required to pass between full and reduced coactions of locally compact groups on C*-algebras, which say, roughly speaking, that one can always do so without changing the crossed-product C*-algebra. Wherever possible we use definitions and constructions that are well-documented and accessible to non-experts, and otherwise we provide full details. We then give a series of applications to illustrate the use of these techniques. We obtain in particular a new version of Mansfield's imprimitivity theorem for full coactions, and prove that it gives a natural isomorphism between crossed-product functors defined on appropriate categories.