Structure Theorems for Bicomodule Algebras Over Quasi Hopf Algebras Weak Hopf Algebras and Braided Hopf Algebras

Abstract

Let H be a quasi-Hopf algebra, a weak Hopf algebra, or a braided Hopf algebra. Let B be an H-bicomodule algebra such that there exists a morphism of H-bicomodule algebras v H → B. Then we can define an object Bco H , which is a left-left Yetter– Drinfeld module over H, having extra properties that allow to make a smash product B^co H #H, which is an H-bicomodule algebra, isomorphic to B.