A categorical interpretation of Yetter-Drinfel'd modules  

作　　者：KAN Haibin and WANG ShuanhongInstitute of Mathematics , Fudan University , Shanghai 200433 , China  Department of Mathematics , Henan Normal University, Xinxiang 453002, China 

出　　处：《Chinese Science Bulletin》1999年第9期771-778,共8页

摘　　要：It is known that any strict tensor category （C, I） can determine a strict braided tensor category Z （ C）, the centre of C. When A is a finite Hopf algebra, Drinfel’d has proved that Z（_AM） is equivalent to _D（A）M as a braided tensor category, where _AM is the left A-module category, and D （A） is the Drinfel’d double of A. This is the categorical interpretation of D （A）.Z（₄M） is proved to be equivalent to the Yetter-Drinfel’ d module category _AY D⁴ as a braided tensor category for any Hopf algebra A. Furthermore, for right A-comodule category M^A , Z（M^A） is proved to be equivalent to the Yetter-Drinfel’ d module category _AY D⁴ as a braided tensor category. But, in the two cases, the Yetter-Drinfel’ d module category _AY D^A has different braided tensor structures.It is known that any strict tensor category (C,?,I) can determine a strict braided tensor categoryZ(C), the centre ofC. WhenA is a finite Hopf algebra, Drinfel’d has proved thatZ( AM) is equivalent toD(A)M as a braided tensor category, whereAM is the left A-module category, andD(A) is the Drinfel’d double ofA. This is the categorical interpretation ofD(A). Z( AM) is proved to be equivalent to the Yetter-Drinfel’d module category,AYD A as a braided tensor category for any Hopf algebraA. Furthermore, for right A-comodule categoryM A, Z(MA) is proved to be equivalent to the Yetter-Drinfel’d module categoryAY DA as a braided tensor category. But,in the two cases, the Yetter-Drinfel’d module categoryAY DA has different braided tensor structures.

关 键 词：Yetter-Drinfel’d module TENSOR CATEGORY equivalence. 

分 类 号：O153[理学—数学]