交换群上Hopf路余代数的结构分类

Structure Classification of Hopf Path Coalgebras over Abelian Groups

设G是群,kG是域k上的群代数.对任意Hopf箭向Q=(G,r),利用右kZ_(u(C))-模的直积范畴(?)M_(kZu(C))与kG-Hopf双模范畴之间的同构,可由^(u(C))(kQ_1)~1上的右kZ_(u(C))-模结构导出在箭向余模kQ_1上的kG-Hopf双模结构.该文讨论在群G分别是2阶循环群与克莱茵四元群时的Hopf路余代数kQ^c的同构分类及其子Hopf代数kG[kQ_1]结构.

Let G be a group and kG be the that the kG-Hopf bimodule category KKGkM^KGKG group algebra of G over a field k. It is well known is equivalent to the direct category ПMkzu（c）. For any Hopf quiver Q = （G, r）, the kG-Hopf bimodule structures on the arrow comodule kQ1 can be derived from the right kZu（c）-module structures on u（C）（kQ1）^1. In this paper, the author discusses the isomorphic classification of Hopf path coalgebra kQc and the structures of Hopf subalgebra of kG[kQ1] of kQ^c in case G is a cyclic group and G is a Klein quaternion group, respectively.