|
Aspects of compact quantum group theory
Author(s):
G.
J.
Murphy;
L.
Tuset
Journal:
Proc. Amer. Math. Soc.
132
(2004),
3055-3067.
MSC (2000):
Primary 46L89, 58B32
Posted:
June 2, 2004
MathSciNet review:
2063127
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
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.
References:
-
- 1.
- E. Abe, Hopf Algebras, Cambridge University Press, Cambridge, 1980. MR 83a:16010
- 2.
- K. Abodayeh and G. J. Murphy, Compact topological semigroups, Proc. Royal Irish Acad. 97A (1997), 131-137. MR 99g:22002
- 3.
- E. Bedos, G. J. Murphy and L. Tuset, Co-amenability of compact quantum groups, J. Geom. Phys. 40 (2001), 130-153. MR 2002m:46100
- 4.
- E. Bedos, G. J. Murphy and L. Tuset, Amenability and coamenability of algebraic quantum groups, International J. Math. and Math. Sci. 31 (2002), 577-601. MR 2003j:46107
- 5.
- V. G. Drinfeld, Quantum groups, Proceedings of the International Congress of Mathematicians, Berkeley (1986), 793-820. MR 89f:17017
- 6.
- M. Enock and J.-M. Schwartz, Kac Algebras and Duality of Locally Compact Groups, Springer, Berlin-Heidelberg, 1992. MR 94e:46001
- 7.
- C. Kassel, Quantum Groups, Springer, Berlin-Heidelberg, 1995. MR 96e:17041
- 8.
- E. C. Lance, Hilbert
 -Modules--A Toolkit for Operator Algebraists, Cambridge University Press, Cambridge, 1995. MR 96k:46100 - 9.
- A. Maes and A. Van Daele, Notes on compact quantum groups, Nieuw Arch. Voor Wisk. 16 (1998), 73-112. MR 99g:46105
- 10.
- G. J. Murphy,
 -Algebras and Operator Theory, Academic Press, San Diego, 1990. MR 91m:46084 - 11.
- A. Van Daele, The Haar measure on a compact quantum group, Proc. Amer. Math. Soc. 123 (1995), 3125-3128. MR 95m:46097
- 12.
- S. Wassermann, Exact
 -Algebras and Related Topics, University Press, National University Seoul, 1994. MR 95b:46081 - 13.
- S. L. Woronowicz, Compact matrix pseudogroups, Comm. Math. Phys. 111 (1987), 613-665. MR 88m:46079
- 14.
- S. L. Woronowicz, Twisted
 groups--an example of a noncommutative differential calculus, Publ. RIMS Kyoto Univ. 23 (1987), 117-181. MR 88h:46130 - 15.
- S. L. Woronowicz, Compact quantum groups, in Symétries Quantiques, North Holland, Amsterdam, 1998, pp. 845-884. MR 99m:46164
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (2000):
46L89, 58B32
Retrieve articles in all Journals with
MSC (2000):
46L89, 58B32
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:
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
Copyright of article:
Copyright
2004,
American Mathematical Society
|
