Aspects of compact quantum group theory

Murphy, G.; Tuset, L.

doi:10.1090/S0002-9939-04-07400-3

Aspects of compact quantum group theory
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by G. J. Murphy and L. Tuset PDF

Proc. Amer. Math. Soc. 132 (2004), 3055-3067 Request permission

Abstract:

We show that if a compact quantum semigroup satisfies certain weak cancellation laws, then it admits a Haar measure, and using this we show that it is a compact quantum group. Thus, we obtain a new characterization of a compact quantum group. We also give a necessary and sufficient algebraic condition for the Haar measure of a compact quantum group to be faithful, in the case that its coordinate $C^*$-algebra is exact. A representation is given for the linear dual of the Hopf $*$-algebra of a compact quantum group, and a functional calculus for unbounded linear functionals is derived.

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