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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Aspects of compact quantum group theory


Authors: G. J. Murphy and L. Tuset
Journal: Proc. Amer. Math. Soc. 132 (2004), 3055-3067
MSC (2000): Primary 46L89, 58B32
Published electronically: June 2, 2004
MathSciNet review: 2063127
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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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Additional Information

G. J. Murphy
Affiliation: Department of Mathematics, National University of Ireland, Cork, Ireland

L. Tuset
Affiliation: Faculty of Engineering, University College, Oslo, Norway

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07400-3
PII: S 0002-9939(04)07400-3
Keywords: Quantum group, Haar measure
Received by editor(s): December 10, 2001
Received by editor(s) in revised form: June 3, 2003
Published electronically: June 2, 2004
Communicated by: David R. Larson
Article copyright: © Copyright 2004 American Mathematical Society