Self-dual modules of semisimple Hopf algebras

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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.
9 pages. Important new result included. See also http://www.mathematik.uni-muenchen.de/~sommerh

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Rings and Algebras, Quantum Algebra, Representation Theory, 16W30

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http://salesiana.dossiersoluciones.com/handle/123456789/61757

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0106254
 http://arxiv.org/abs/math/0106254
 J. Algebra 257 (2002), 88-96

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arXiv