Nichols algebras over weak Hopf algebras

In this paper, we study a Yetter-Drinfeld module V over a weak Hopf algebra ℍ. Although the category of all left ℍ-modules is not a braided tensor category, we can define a Yetter-Drinfeld module. Using this Yetter-Drinfeld modules V, we construct Nichols algebra B(V) over the weak Hopf algebra ℍ, and a series of weak Hopf algebras. Some results of [8] are generalized.