Self-dual modules of semisimple Hopf algebras

Yevgenia Kashina; Yorck Sommerhaeuser; Yongchang Zhu

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Self-dual modules of semisimple Hopf algebras

Yevgenia Kashina·Yorck Sommerhaeuser·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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Yevgenia Kashina, Yorck Sommerhaeuser, Yongchang Zhu. 2001-07-03. Self-dual modules of semisimple Hopf algebras. https://arxiv.org/abs/math/0106254

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