Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

A commuting pair in Hopf Algebras

Author(s): 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 $\text {dim } (H)$ .

References:

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[Z]: Y.Zhu, Hopf Algebras of Prime Dimension, Intern. Math. Res. Notices No.1 (1994), 53-59. MR 94j:16072

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