Coaction functors

TL;DR

This paper introduces and studies coaction functors related to crossed-product functors in the context of the Baum-Connes conjecture, focusing on those induced by large ideals of the Fourier-Stieltjes algebra.

Contribution

It defines and analyzes a class of coaction functors, highlighting their role in understanding crossed-product functors and their relation to the Baum-Connes conjecture.

Findings

Most important coaction functors are induced by large ideals of the Fourier-Stieltjes algebra.

Open problem: whether the minimal exact and Morita compatible crossed-product functor is induced by a large ideal.

Abstract

A certain type of functor on a category of coactions of a locally compact group on C*-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.