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

Year 2009, Volume: 6 Issue: 6, 74 - 94, 01.12.2009

Bing-liang Shen Shuan-hong Wang

Abstract

Let L be a weak Hopf algebra with a bijective antipode SL 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 L LWYD in the sense of [1], then its dual H∗ is also a weak Hopf algebra in L LWYD. Also we will apply above result to the representations category Rep(L) = LM of a quasitriangular weak Hopf algebra L.

Keywords

Weak Hopf algebra, weak Yetter-Drinfeld categories, weak (co)module (co)algebras, duality

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• Bing-liang Shen and Shuan-hong Wang Department of Mathematics Southeast University Nanjing, Jiangsu 210096, P. R. of China e-mail: [e-mail] (B.L. Shen), [e-mail] (S.H. Wang)