Hopf C*-algebras

Details Hopf C*-algebras Hopf C*-algebras

1999-07-06

arxiv.org/abs/math/9907030v1

Proc. London Math. Soc. (3) 82, 2001, 337-384.

Mathematics

Operator Algebras

50 pages, LaTeX 2e

Scientific paper

In this paper we introduce the notion of a Hopf C*-algebra and construct the counit and antipode. A Hopf C*-algebra is a C*-algebra with comultiplication satisfying some extra condition which makes possible the construction of the counit and antipode. The leading example is of course the C*-algebra of continuous, vanishing at infinity functions on a locally compact group. Also locally compact quantum groups will be examples. We include several formulas for the counit and antipode which are familiar from Hopf algebra theory.

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