|
Some properties of factorizable Hopf algebras
Author(s):
H.-J.
Schneider
Journal:
Proc. Amer. Math. Soc.
129
(2001),
1891-1898.
MSC (1991):
Primary 16W30;
Secondary 16G10
Posted:
January 23, 2001
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
A direct proof without modular category theory is given of a recent theorem of Etingof and Gelaki (1998) on the dimensions of irreducible representations. Factorizable Hopf algebras are characterized in terms of their Drinfeld double, and their character rings and the group-like elements of their duals are described.
References:
-
- [D]
- V. G. Drinfeld, On almost cocommutative Hopf algebras, Leningrad Math. J. 1 (1990), 321-342.
- [EG]
- P. Etingof and S. Gelaki, Some properties of finite-dimensional semisimple Hopf algebras, Mathematical Research Letters 5 (1998), 191-197. MR 99e:16050
- [K]
- C. Kassel, Quantum Groups, Springer, GTM 155, New York, 1995. MR 96e:17041
- [Ki]
- A. A. Kirillov Jr., On an inner product in modular categories, J. Amer. Math. Soc. 9 (1996), 1135-1169. MR 97f:18007
- [LR]
- R. G. Larson and D. E. Radford, Finite-dimensional cosemisimple Hopf algebras in characteristic 0 are semisimple, J. Alg. 117 (1988), 267-289. MR 89k:16016
- [L]
- M. Lorenz, On the class equation for Hopf algebras, Proc. Amer. Math. Soc. 126 (1998), 2841-2844. MR 99a:16033
- [M]
- S. Montgomery, Hopf algebras and their actions on rings, CBMS Lecture Notes 82, Amer. Math. Soc., 1993. MR 94i:16019
- [OS]
- U. Oberst, H.-J. Schneider, Über Untergruppen endlicher algebraischer Gruppen, manuscripta math. 8 (1973), 217-241. MR 50:339
- [R93]
- D. E. Radford, Minimal quasitriangular Hopf algebras, J. Algebra 157 (1993), 285-315. MR 94c:16052
- [R94]
- D. E. Radford, On Kauffman's knot invariants arising from finite-dimensional Hopf algebras, in: Advances in Hopf Algebras, Lecture Notes in Pure and Applied mathematics, Dekker, New York, 1994, 205-266. MR 96g:57013
- [RS]
- N. Y. Reshetikhin, M. A. Semenov-Tian-Shansky, Quantum R-matrices and factorization problems, Journal Geometry Physics 5 (1988), 533-550. MR 92g:17019
- [TZ]
- Y. Tsang, Y. Zhu, On the Drinfeld double of a Hopf algebra, preprint, 1998.
- [T]
- V. Turaev, Quantum invariants of knots and 3-manifolds, de Gruyter Studies in Mathematics 18, Walter de Gruyter & Co., Berlin, 1994.
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(1991):
16W30,
16G10
Retrieve articles in all Journals with MSC
(1991):
16W30,
16G10
Additional Information:
H.-J.
Schneider
Affiliation:
Mathematisches Institut, Universität München, Theresienstraße 39, D-80333 München, Germany
Email:
hanssch@rz.mathematik.uni-muenchen.de
DOI:
10.1090/S0002-9939-01-05787-2
PII:
S 0002-9939(01)05787-2
Keywords:
Factorizable Hopf algebras,
irreducible representations,
Drinfeld double
Received by editor(s):
May 20, 1999
Received by editor(s) in revised form:
October 22, 1999
Posted:
January 23, 2001
Communicated by:
Ken Goodearl
Copyright of article:
Copyright
2001,
American Mathematical Society
|
Comments: webmaster@ams.org