Naturality and induced representations

Authors

Siegfried Echterhoff, University of Munster
S Kaliszewski, Arizona State University
John Quigg, University of WollongongFollow
Iain Raeburn, University of NewcastleFollow

RIS ID

19110

Publication Details

Echterhoff, S., Kaliszewski, S., Quigg, J. & Raeburn, I. (2000). Naturality and induced representations. Bulletin of the Australian Mathematical Society, 61 (3), 415-438.

Abstract

We show that induction of covariant representations for C^*-dynamical systems is natural in the sense that it gives a natural transformation between certain crossed-product functors. This involves setting up suitable categories of C^*-algebras and dynamical systems, and extending the usual constructions of crossed products to define the appropriate functors. From this point of view, Green's Imprimitivity Theorem identifies the functors for which induction is a natural equivalence. Various special cases of these results have previously been obtained on an ad hoc basis.