Self-dual modules of semisimple Hopf algebras. (Q1858245)

The authors generalize a classical result of W. Burnside by showing that, over an algebraically closed field of characteristic zero, a semisimple Hopf algebra that has a nontrivial self-dual simple module must be even dimensional. As an application, it is shown that under the same assumptions, a semisimple Hopf algebra having a simple module of even dimension must itself have even dimension.