A commuting pair in Hopf algebras
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- by Yongchang Zhu PDF
- Proc. Amer. Math. Soc. 125 (1997), 2847-2851 Request permission
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 $\text {dim } (H)$.References
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Additional Information
- Yongchang Zhu
- Affiliation: Department of Mathematics, Hong Kong University of Science & Technology, Clear Water Bay, Hong Kong
- MR Author ID: 321916
- Received by editor(s): December 6, 1995
- Received by editor(s) in revised form: April 30, 1996
- Communicated by: Ken Goodearl
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 2847-2851
- MSC (1991): Primary 16W30
- DOI: https://doi.org/10.1090/S0002-9939-97-03988-9
- MathSciNet review: 1402892