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Selfdual Modules of Semisimple Hopf Algebras
Yevgenia Kashina
Yorck Sommerhäuser
Yongchang Zhu


Abstract
We prove that, over an algebraically closed field of characteristic zero, a semisimple Hopf algebra that has a nontrivial selfdual 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.




Contents
 The Drinfel'd double
 The evaluation form
 The FrobeniusSchur theorem
 Selfdual modules
 Simple modules of even dimension
 The case of positive characteristic



