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.
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)
