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Self-dual modules of semisimple Hopf algebras

✍ Scribed by Yevgenia Kashina; Yorck Sommerhäuser; Yongchang Zhu

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
89 KB
Volume
257
Category
Article
ISSN
0021-8693

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✦ Synopsis

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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