弱Hopf群余代数上的Yetter-Drinfeld模及中心构建

上海大学学报(自然科学版) ›› 2010, Vol. 16 ›› Issue (3): 248-252.

弱Hopf群余代数上的Yetter-Drinfeld模及中心构建

张翔,王卿文

（1.上海大学理学院,上海 200444; 2.遵义师范学院数学系,贵州遵义 563000)

出版日期:2010-06-28 发布日期:2010-06-28

Yetter-Drinfeld Module over Weak Hopf π Coalgebra and Center Construction

ZHANG Xiang,WANG Qing-wen

(1. College of Sciences, Shanghai University, Shanghai 200444, China;2. Department of Mathematics, Zunyi Normal College, Zunyi 563000, Guizhou, China)

Online:2010-06-28 Published:2010-06-28

摘要/Abstract

摘要：

研究弱Hopf群余代数上的Yetter-Drinfeld模，探讨其在弱Hopf群余代数上的性质,并给出它的等价条件.同时介绍单项范畴、单项范畴上的中心及弱中心,在此基础上,研究它与Yetter-Drinfeld模的关系.最后,证明在一定条件下二者是同构的，从而对弱Hopf群余代数及相关结构进行了更进一步的刻画.

关键词: Yetter-Drinfeld模;弱中心;同构

Abstract:

This paper studies Yetter-Drinfeld modules over weak Hopf π coalgebra, discusses its properties over weak Hopf π coalgebra and gives its equivalent condition. The paper introduces monoidal categories, center and weak center over monoidal categories, which are divided into left and right centers. Based on these, the relations between the center and the Yetter-Drinfeld modules categories are studied, and it is proved that the center and the Yetter-Drinfeld module categories are isomorphic. Weak Hopf π coalgebra and its structure are further studied. 

Key words: Yetter-Drinfeld modules; weak center; isomorphic

张翔,王卿文. 弱Hopf群余代数上的Yetter-Drinfeld模及中心构建[J]. 上海大学学报(自然科学版), 2010, 16(3): 248-252.

ZHANG Xiang,WANG Qing-wen. Yetter-Drinfeld Module over Weak Hopf π Coalgebra and Center Construction[J]. Journal of Shanghai University（Natural Science Edition）, 2010, 16(3): 248-252.