A commuting pair in Hopf algebras

Zhu, Yongchang

doi:10.1090/S0002-9939-97-03988-9

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 $\text {dim } (H)$.

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