ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

2. Algebra

1991 MS Classification: 16W30 Schauenburg, Peter, Universität München, Germany Hopf algebras with a weak projection Let H be a Hopf algebra, and H′ ⊂ H a Hopf subalgebra. If the inclusion map of H′ into H splits as a Hopf algebra map, a well-known result of Radford describes how H is decomposed as a tensor product of H′ with another factor, which, in more recent language, is a Hopf algebra in the braided category of Yetter-Drinfeld modules over H′. We describe the structure of H in the case when only a splitting map for the inclusion with weaker properties is assumed to exist, and discuss some applications.