Title: Hopf Algebras and their Frobenius-Schur Indicators

Abstract: A Hopf algebra is an algebra which permits the formation of the tensor product of two modules. Moreover, every module has a dual, and therefore it is possible for a module to be self-dual. Whether or not this is the case is detected by a certain invariant, the so-called Frobenius-Schur indicator. We discuss these indicators and their generalizations and applications, especially their application in the proof of a version of Cauchy's theorem for Hopf algebras. 

The talk is based on joint work with Y. Kashina and Y. Zhu. It is intended for a general audience; in particular, no knowledge of Hopf algebras will be assumed.