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 Bco(H)#H, which is an H-bicomodule algebra, isomorphic to B.