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