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

Authors

Astrid An Huef, University of Otago
John Quigg, Arizona State Univjersity
Iain Raeburn, University of WollongongFollow
Dana P. Williams, Dartmouth CollegeFollow

RIS ID

34548

Publication Details

An Huef, A., Quigg, J., Raeburn, I. & Williams, D. P. (2011). Full and reduced coactions of locally compact groups on C*-algebras. Expositiones Mathematicae, 29 (1), 3-23.

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.