WEAK HOPF ALGEBRA DUALITY IN WEAK YETTER-DRINFELD CATEGORIES AND APPLICATIONS

Let L be a weak Hopf algebra with a bijective antipode S-L in the sense of [3]. In this paper we show that if H is a finite-dimensional weak Hopf algebra in the weak Yetter-Drinfeld category LLWYD in the sense of [1], then its dual H* is also a weak Hopf algebra in LLWYD. Also we will apply above result to the representations category Rep(L) = L-M of a quasitriangular weak Hopf algebra L.