BICOVARIANT DIFFERENTIAL CALCULI ON A WEAK HOPF ALGEBRA

Abstract

Let $H$ be a weak Hopf algebra with bijective antipode. In this paper we follow Woronowicz's fundamental method to characterize bicovariant differential calculi on $H$. We show that there exists a 1-1 correspondence between bicovariant differential calculi and some right ideals of $H$ contained in $ ker \varepsilon_s $ such that these ideals are right $H$-comodules with coadjoint maps, where $\varepsilon_s$ is the source map of $H$. This is a generalization of well-known Woronowicz's theorem about bicovariant differential calculi on quantum groups.