Coactions and Fell bundles

Details Coactions and Fell bundles Coactions and Fell bundles

2009-09-17

arxiv.org/abs/0909.3259v1

Mathematics

Operator Algebras

39 Pages

Scientific paper

We show that if $\AA$ is a Fell bundle over a locally compact group $G$, then there is a natural coaction $\delta$ of $G$ on the Fell-bundle $C^*$-algebra $C^*(G,\AA)$ such that if $\hat{\delta}$ is the dual action of $G$ on the crossed product $C^*(G,\AA) \rtimes_{\delta} G$, then the full crossed product $(C^*(G,\AA) \rtimes_{\delta}G)\rtimes_{\hat{\delta}}G$ is canonically isomorphic to $C^*(G,\AA) \otimes\KK(L^2(G))$. Hence the coaction $\delta$ is maximal.

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