Construction of semisimple category over generalized Yetter-Drinfeld modules  

广义Yetter-Drinfeld模上半单范畴的构造(英文)

作　　者：张晓辉[1] 王栓宏[1] 

机构地区：[1]东南大学数学系,南京211189

出　　处：《Journal of Southeast University(English Edition)》2013年第4期467-469,共3页东南大学学报（英文版）

基　　金：The National Natural Science Foundation of China(No.11371088);the Fundamental Research Funds for the Central Universities(No.3207013906);the Natural Science Foundation of Jiangsu Province(No.BK2012736)

摘　　要：Let H be a commutative, noetherian, semisimple and cosemisimple Hopf algebra with a bijective antipode over a field k. Then the semisimplicity of YD（H） is considered, where YD （H） means the disjoint union of the category of generalized Yetter-Drinfeld modules nYD^H（ α, β） for any α, β E Aut Hopf（H）. First, the fact that YD（H） is closed under Mor is proved. Secondly, based on the properties of finitely generated projective modules and semisimplicity of H, YD（H） satisfies the exact condition. Thus each object in YD（H） can be decomposed into simple ones since H is noetherian and cosemisimple. Finally, it is proved that YD （H） is a sernisimple category.设H是域k上的可换、诺特、半单、余半单的Hopf代数,且具有双射对极.考虑了其上YD(H)范畴的半单性,其中YD(H)是H上的广义Yetter-Drinfeld模范畴H YDH(α,β)(其中α,β∈Aut Hopf(H))的无交并.首先证明了YD(H)是一个对态射集封闭的范畴;然后利用有限生成投射模的性质和H的半单性,可得YD(H)是满足正合性条件的;进而由H是诺特、余半单的Hopf代数,得到YD(H)中的对象都可分解为单对象的直和.最终得到YD(H)是一个半单范畴.

关 键 词：semisimple Hopf algebra semisimple category generalized Yetter-Drinfeld module 

分 类 号：O153.3[理学—数学]