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

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.Comment: 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 proo

Full duality for coactions of discrete groups

Using the strong relation between coactions of a discrete group G on C*-algebras and Fell bundles over G, we prove a new version of Mansfield's imprimitivity theorem for coactions of discrete groups. Our imprimitivity theorem works for the universally defined full crossed products and arbitrary subgroups of G, as opposed to the usual theory which uses the spatially defined reduced crossed products and normal subgroups of G. Moreover, our theorem factors through the usual one by passing to appropriate quotients. As applications we show that a Fell bundle over a discrete group is amenable in the sense of Exel if and only if the double dual action is amenable in the sense that the maximal and reduced crossed products coincide. We also give a new characterization of induced coactions in terms of their dual actions.Comment: 18 page

C*-actions of r-discrete groupoids and inverse semigroups

Groupoid actions on C*-bundles and inverse semigroup actions on C*-algebras are closely related when the groupoid is r-discrete.Comment: LaTeX-2e, 18 pages, uses pb-diagram.st