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Compact quantum groups and group duality

✍ Scribed by Xiu-Chi Quan

Publisher: Springer Netherlands
Year: 1991
Tongue: English
Weight: 791 KB
Volume: 25
Category: Article
ISSN: 0167-8019
DOI: 10.1007/bf00047006

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✦ Synopsis

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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