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Coactions and Fell bundles. (English) Zbl 1226.46060

Summary: We show that for any Fell bundle \(\mathcal A\) over a locally compact group \(G\), there is a natural coaction \(\delta\) of \(G\) on the Fell-bundle \(C^*\)-algebra \(C^*(G,{\mathcal A})\) such that the full crossed product \((C^*(G,{\mathcal A})\rtimes_\delta G)\rtimes_{\hat\delta} G\) by the dual action \(\hat \delta\) of \(G\) is canonically isomorphic to \(C^*(G,{\mathcal A})\otimes{\mathcal K}(L^2(G))\).
Hence the coaction \(\delta\) is maximal.

MSC:

46L55 Noncommutative dynamical systems
46M15 Categories, functors in functional analysis
18A25 Functor categories, comma categories
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