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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A commuting pair in Hopf Algebras

Author: Yongchang Zhu
Journal: Proc. Amer. Math. Soc. 125 (1997), 2847-2851
MSC (1991): Primary 16W30
MathSciNet review: 1402892
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Abstract: We prove that if $H$ is a semisimple Hopf algebra, then the action of the Drinfeld double $D(H)$ on $H$ and the action of the character algebra on $H$ form a commuting pair. This result and a result of G. I. Kats imply that the dimension of every simple $D(H)$-submodule of $H$ is a divisor of $\text {dim } (H)$.

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Yongchang Zhu
Affiliation: Department of Mathematics, Hong Kong University of Science & Technology, Clear Water Bay, Hong Kong

Received by editor(s): December 6, 1995
Received by editor(s) in revised form: April 30, 1996
Communicated by: Ken Goodearl
Article copyright: © Copyright 1997 American Mathematical Society