交换群上Hopf路余代数的结构分类

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∏_C∈K(G) MkZ_u(C)与kG-Hopf双模范畴^kG_kG M^kG_kG之间的同构, 可由^u(C)(kQ₁)¹上的右kZ_u(C) -模结构导出在箭向余模kQ₁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kGkQ₁]结构.

Structure Classification of Hopf Path Coalgebras over Abelian Groups

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 M^kG_kG is equivalent to the direct category ∏_C ∈ K(G) MkZ_u(C) . For any Hopf quiver Q=(G, r), the kG-Hopf bimodule structures on the arrow comodule kQ₁ can be derived from the right kZ_u(C)-module structures on ^u(C)(kQ₁)¹. In this paper, the author discusses the isomorphic classification of Hopf path coalgebra kQ^c and the structures of Hopf subalgebra of kGkQ₁] of kQ^c in case G is a cyclic group and G is a Klein quaternion group, respectively.