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Compact group actions on \(C^*\)-algebras. (English) Zbl 0689.46020

This work is a contribution to the formulation of an abstract duality theory for compact groups into the framework of \(C^*\)-algebras. More specifically it treats certains aspects of the spectral analysis of the actions \(\alpha\) of compact groups G on infinite \(C^*\)-algebras B by looking at \(\alpha\)-stable Hilbert spaces H in B. Some variants of the Tannaka-Krein theorem are proved in this context, given conditions for a compact group G to agree with the stabilizer in Aut B of the fixed point algebra. A Galois correspondence between some subalgebras of B and normal subgroups of G is constructed, and the structure of the relative commutant is studied. The paper ends with the construction of examples illustrating the setting of this work.
Reviewer: G.Loupias

MSC:

46L55 Noncommutative dynamical systems
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