A note on ribbon elements of Hopf group-coalgebras  

关于Hopf群余代数ribbon元的注记（英文）

作　　者：赵晓凡[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)》2015年第2期294-296,共3页东南大学学报（英文版）

基　　金：The National Natural Science Foundation of China(No.11371088);the Natural Science Foundation of Jiangsu Province(No.BK2012736);the Fundamental Research Funds for the Central Universities(No.KYZZ0060)

摘　　要：Let G be a discrete group with a neutral element and H be a quasitriangular Hopf G-coalgebra over a field k. Then the relationship between G-grouplike elements and ribbon elements of H is considered. First, a list of useful properties of a quasitriangular Hopf G-coalgebra and its Drinfeld elements are proved. Secondly, motivated by the relationship between the grouplike and ribbon elements of a quasitriangular Hopf algebra, a special kind of G-grouplike elements of H is defined. Finally, using the Drinfeld elements, a one-to-one correspondence between the special G-grouplike elements defined above and ribbon elements is obtained.设G是一个带有单位元的离散群,H是域k上的拟三角Hopf G-余代数.考虑了H的G-群像元和ribbon元之间的关系.首先证明了拟三角Hopf G-余代数以及它的Drinfeld元的一些重要性质.受到Hopf代数中群像元和ribbon元之间关系的启发,定义了一类特殊的G-群像元.最后利用Drinfeld元得到了所定义的特殊的G-群像元和ribbon元之间的一个一一对应关系.

关 键 词：quasitriangular Hopf G-coalgebra G-grouplikeelement ribbon element Drinfeld element 

分 类 号：O153.3[理学—数学]