Imprimitivity for $C^*$-Coactions of Non-Amenable Groups

TL;DR

This paper establishes conditions under which Mansfield imprimitivity holds for full coactions of non-amenable groups, extending the theory to broader classes of coactions and demonstrating its stability under various operations.

Contribution

It provides a new criterion ensuring Mansfield imprimitivity for non-amenable groups and shows its invariance under key transformations.

Findings

Mansfield imprimitivity holds if the subgroup is amenable or the coaction is normal.

The condition is stable under Morita equivalence and other coaction modifications.

The result extends imprimitivity theory to non-amenable group actions.

Abstract

We give a condition on a full coaction $(A,G,\delta)$ of a (possibly) nonamenable group $G$ and a closed normal subgroup $N$ of $G$ which ensures that Mansfield imprimitivity works; i.e. that $A\times_{\delta{\vert}} G/N$ is Morita equivalent to $A\times_\delta G\times_{\deltahat,r} N$. This condition obtains if $N$ is amenable or $\delta$ is normal. It is preserved under Morita equivalence, inflation of coactions, the stabilization trick of Echterhoff and Raeburn, and on passing to twisted coactions.