交换群上Hopf路余代数的结构分类(Ⅲ)

Construction Classification of Hopf Path Coalgebras over Dihedral Group(Ⅲ)

从Hopf quiver出发,借助于右kZu(C)-模的直积范畴∏C∈K(G)MkZu(C)与kG-Hopf双模范畴kGkGMkkGG之间的同构,就G为二面体群D2时,给出了Hopf路余代数kQC的同构分类及其子Hopf代数kG[kQ1]的结构.

Let G be a group and kG be the group algebra of G over a field k. It is well known that the kG-Hopf bimodule category kG↑ kG MkG↑ kG is equivalent to the direct product category ПC∈K（G）MkZu（C）, where K（G） is the set of conjugate classes in G, u：K（G）→G is a map such that u（C）∈C for any C∈K（G）, Zu（C） ： {g∈G｜gu（C）=u（C）g} and MkZu（C） denoted the category of right kZu（C） modules. In this paper, the distinct isomorphic classication of co-path Hopf algebra kQ^c and the structure of Hopf subalgehra of kG[kQ1] are discussed when G=D2 ,a dihedral group.