Actions of Hopf Algebras in Categories of Yetter-Drinfeld Modules

Abstract

Let H be a k-Hopf algebra and A a Hopf algebra in the category of Yetter-Drinfeld modules over H. We define the notion of an action of A on an H-module algebra and study inner and outer actions. Especially we prove that for each action of A there is a largest inner Hopf subalgebra in if we assume pointedness. Furthermore we prove the existence of non-trivial invariants of inner or outer actions of A. This gives new information about actions of biproducts.