Coaction functors

S. Kaliszewski, Magnus B. Landstad and John Quigg

Vol. 284 (2016), No. 1, 147–190

DOI: 10.2140/pjm.2016.284.147

Abstract

A certain type of functor on a category of coactions of a locally compact group on $C^{\ast }$-algebras is introduced and studied. These functors are intended to help in the study of the crossed-product functors that have been recently introduced in relation to the Baum–Connes conjecture. The most important coaction functors are the ones induced by large ideals of the Fourier–Stieltjes algebra. It is left as an open problem whether the “minimal exact and Morita compatible crossed-product functor” is induced by a large ideal.

Keywords

crossed product, action, coaction, Fourier–Stieltjes algebra, exact sequence, Morita compatible

Mathematical Subject Classification 2010

Primary: 46L55

Secondary: 46M15

Milestones

Received: 6 June 2015

Revised: 31 March 2016

Accepted: 4 April 2016

Published: 10 July 2016