1999/07/06 by Stefaan Vaes, Alfons Van Daele
Mathematics · #math.OA #math.FA
published as Proc. London Math. Soc. (3) 82, 2001, 337-384. · 50 pages, LaTeX 2e
arxiv created 1999/07/06 · arxiv updated 2009/11/30
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.