Self-dual 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 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.
Contents
- The Drinfel'd double
- The evaluation form
- The Frobenius-Schur theorem
- Self-dual modules
- Simple modules of even dimension
- The case of positive characteristic
