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

Abstract

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

23 pages, LaTeX 2e, requires amscd.sty and pb-diagram.sty. Revisions include deletion of false Lemma 2.3 and amendment of proofs of Proposition 2.4 and Theorem 4.1, which had relied on the false lemma or its proof