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Title: Self-dual modules of semisimple Hopf algebras
Authors: Kashina, Yevgenia
Sommerhaeuser, Yorck
Zhu, Yongchang
Keywords: Rings and algebras
Quantum algebra
Representation theory
Issue Date: Nov-2002
Citation: Journal of Algebra, v. 257, issue no. 1, 1 November 2002, P. 88-96.
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.
Rights: Published in Journal of Algebra, (c)2002 Elsevier Science
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