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Self-dual Modules of Semisimple Hopf Algebras
Yevgenia Kashina      
Yorck Sommerhäuser
Yongchang Zhu
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Abstract
We prove that, over an algebraically closed field of characteristic zero, a semisimple Hopf algebra that has a nontrivial self-dual simple module must have even dimension. This generalizes a classical result of W. Burnside. As an application, we show under the same assumptions that a semisimple Hopf algebra that has a simple module of even dimension must itself have even dimension.
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Contents
- The Drinfel'd double
- The evaluation form
- The Frobenius-Schur theorem
- Self-dual modules
- Simple modules of even dimension
- The case of positive characteristic
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