Compact quantum groups and group duality |
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Authors: | Xiu-Chi Quan |
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Institution: | (1) Department of Mathematics, University of Iowa, 52242-1466 Iowa City, IA, U.S.A. |
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Abstract: | In this paper, we consider the *-representations of compact quantum groups and group duality. The main results in the paper are: (1) there is a one-to-one correspondence between the *-representations of compact quantum groups and *-representations of the dual Banach *-algebra; (2) the category of commutative compact quantum groups (semigroups) is a dual category to the category of compact groups (semigroups); (3) the dual category of the category of locally compact groups (semigroups) is the category of commutative Hopf C*-algebras with a particular property. Our group duality has the flavor of a Gelfand-Naimark type theorem for compact quantum groups, and for Hopf C*-algebras. |
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Keywords: | 16S80 17B37 22D25 46L89 47A67 |
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