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The $p^n$ theorem for semisimple Hopf algebras


Author: Akira Masuoka
Journal: Proc. Amer. Math. Soc. 124 (1996), 735-737
MSC (1991): Primary 16W30
DOI: https://doi.org/10.1090/S0002-9939-96-03147-4
MathSciNet review: 1301036
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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

DOI: https://doi.org/10.1090/S0002-9939-96-03147-4
Received by editor(s): April 18, 1994
Received by editor(s) in revised form: September 29, 1994
Communicated by: Ken Goodearl
Article copyright: © Copyright 1996 American Mathematical Society

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