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On the class equation for Hopf algebras
Author(s):
Martin
Lorenz
Journal:
Proc. Amer. Math. Soc.
126
(1998),
2841-2844.
MSC (1991):
Primary 16W30;
Secondary 16G10
MathSciNet review:
1452811
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Abstract:
We give a simple proof of the Kac-Zhu class equation for semisimple Hopf algebras over an algebraically closed field of characteristic 0.
References:
- [CR]
- C. W. Curtis and I. Reiner, Methods of Representation Theory, Vol. 1, Wiley-Interscience, New York, 1981. MR 90k:20001
- [K]
- G. I. Kac, Certain arithmetic properties of ring groups, Functional Anal. Appl. 6 (1972), 158-160. MR 46:3687
- [LR]
- R. G. Larson and D. E. Radford, Semisimple cosemisimple Hopf algebras, Amer. J. Math. 109 (1987), 187-195. MR 89a:16011
- [LS]
- R. G. Larson and M. E. Sweedler, An associative orthogonal bilinear form for Hopf algebras, Amer. J. Math. 91 (1969), 75-94. MR 39:1523
- [L]
- M. Lorenz, Representations of finite dimensional Hopf algebras, J. Algebra 188 (1997), 476-505. CMP 97:08
- [M]
- A. Masuoka, Some further classification results of semisimple Hopf algebras, Commun. Algebra 24 (1996), 307-329. MR 96k:16070
- [S]
- H.-J. Schneider, Lectures on Hopf Algebras, Lecture Notes, Universidad Nacional de Cordoba, 1995.
- [Z]
- Y. Zhu, Hopf algebras of prime dimension, Internat. Math. Res. Notices 1 (1994), 53-59. MR 94j:16072
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Additional Information:
Martin
Lorenz
Affiliation:
Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122-6094
Email:
lorenz@math.temple.edu
DOI:
10.1090/S0002-9939-98-04392-5
PII:
S 0002-9939(98)04392-5
Keywords:
Hopf algebra,
Grothendieck ring,
character algebra,
idempotent
Received by editor(s):
December 16, 1996
Received by editor(s) in revised form:
March 13, 1997
Additional Notes:
Research supported in part by NSF Grant DMS-9400643.
Communicated by:
Ken Goodearl
Copyright of article:
Copyright
1998,
American Mathematical Society
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