## 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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### References:

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