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The $p^n$ theorem for semisimple Hopf algebras

Author(s): Akira Masuoka
Journal: Proc. Amer. Math. Soc. 124 (1996), 735-737.
MSC (1991): Primary 16W30
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Abstract: We give an algebraic version of a result of G. I. Kac, showing that a semisimple Hopf algebra $A$ of dimension $p^n$, where $p$ is a prime and $n>0$, over an algebraically closed field of characteristic 0 contains a non-trivial central group-like. As an application we prove that, if $n=2$, $A$ is isomorphic to a group algebra.

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Additional Information:

Akira Masuoka
Affiliation: Department of Mathematics, Shimane University, Matsue, Shimane 690, Japan

DOI: 10.1090/S0002-9939-96-03147-4
PII: S 0002-9939(96)03147-4
Received by editor(s): April 18, 1994
Received by editor(s) in revised form: September 29, 1994
Communicated by: Ken Goodearl
Copyright of article: Copyright 1996, American Mathematical Society

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