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A new duality theory for compact groups. (English) Zbl 0691.22002

Authors’ summary: “The Tannaka-Krein duality theory characterizes the category \({\mathcal H}(G)\) of finite-dimensional continuous, unitary representations of a compact group as a subcategory of the category of Hilbert spaces. We prove a more powerful result characterizing \({\mathcal H}(G)\) as an abstract category: Every strict symmetric monoidal \(C^*\)- category with conjugates which has subobjects and direct sums and for which the \(C^*\)-algebra of endomorphisms of the monoidal unit reduces to the complex numbers is isomorphic to a category \({\mathcal H}(G)\) for a compact group G unique up to isomorphism.”
Reviewer: J.B.Cooper

MSC:

22C05 Compact groups
46L99 Selfadjoint operator algebras (\(C^*\)-algebras, von Neumann (\(W^*\)-) algebras, etc.)
22D10 Unitary representations of locally compact groups
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