A commuting pair in Hopf Algebras

Author:
Yongchang Zhu

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

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that if is a semisimple Hopf algebra, then the action of the Drinfeld double on and the action of the character algebra on form a commuting pair. This result and a result of G. I. Kats imply that the dimension of every simple -submodule of is a divisor of .

**[D]**V.G.Drinfeld,*Quantum Groups*, Proc. Int. Cong. Math, Berkeley (1986), 789-820. MR**89f:17017****[K]**G.I.Kats,,*Certain Arithmetic Properties of Ring Groups*, Functional Anal. Appl.**6**(1972), 158-160.**[LR]**R.G.Larson and D.E.Radford,*Semisimple cosemisimple Hopf Algebras*, Amer.J.Math**110**(1988), 381-385. MR**89a:16011****[M]**S. Montgomery,*Hopf Algebras and Their Actions on Rings*, AMS, 1993. MR**94i:16019****[R]**D.E. Radford,*On the Antipode of a Semisimple Hopf Algebra*, J.Algebra**88**(1984), 66-88. MR**85i:16012****[Z]**Y.Zhu,*Hopf Algebras of Prime Dimension*, Intern. Math. Res. Notices**No.1**(1994), 53-59. MR**94j:16072**

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Additional Information

**Yongchang Zhu**

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

DOI:
https://doi.org/10.1090/S0002-9939-97-03988-9

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