Summary
The Tannaka-Krein duality theory characterizes the category 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 ℋ(G) as an abstract category: every strict symmetric monoidalC *-category with conjugates which has subobjects and direct sums and for which theC *-algebra of endomorphisms of the monoidal unit reduces to the complex numbers is isomorphic to a category ℋ(G) for a compact groupG unique up to isomorphism.
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Research supported by the Ministero della Pubblica Istruzione and CNR-GNAFA
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Doplicher, S., Roberts, J.E. A new duality theory for compact groups. Invent Math 98, 157–218 (1989). https://doi.org/10.1007/BF01388849
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DOI: https://doi.org/10.1007/BF01388849