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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
Posted:
June 2, 2004
MathSciNet review:
2063127
Full-text PDF Free Access
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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  -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
Posted:
June 2, 2004
Communicated by:
David R. Larson
Article copyright:
© Copyright 2004 American Mathematical Society
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