Structure theory for Yetter-Drinfel'd Hopf algebras
by
Yorck Sommerhäuser
Universität München, Deutschland (Germany)

Yetter-Drinfel'd Hopf algebras are Hopf algebras in a certain quasisymmetric monoidal category. They give rise to ordinary Hopf algebras via the Radford biproduct construction.

In the talk, we consider Yetter-Drinfel'd Hopf algebras over groups of prime order that are commutative and semisimple as algebras and cocommutative cosemisimple as coalgebras. For these algebras, we outline the proof of the following structure theorem: They can be decomposed into a tensor product of two group rings of abelian groups. The coalgebra structure is the usual tensor product coalgebra structure, whereas the algebra structure is a crossed product multiplication. This theorem has several applications in the classification program for semisimple Hopf algebras.

Homepage of Yorck Sommerhäuser

Date received: November 18, 1998

Copyright © 1998 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cabw-28.