Self-dual modules of semisimple Hopf algebras

Details Self-dual modules of semisimple Hopf algebras Self-dual modules of semisimple Hopf algebras

2001-06-29

arxiv.org/abs/math/0106254v2

J. Algebra 257 (2002), 88-96

Mathematics

Rings and Algebras

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

Scientific paper

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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