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

S. Kaliszewski·John Quigg
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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.

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S. Kaliszewski, John Quigg. 1996-04-26. Imprimitivity for $C^*$-Coactions of Non-Amenable Groups. https://arxiv.org/abs/funct-an/9602003

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