中文摘要：

本文研究了Hopf代数的构造问题.利用模范畴和箭图,获得了当G是二面体群D_2这一4阶交换群时的Hopf路余代数kQ~c的同构分类及其子Hopf代数kG[kQ_1]的结构,推广了当G是2阶循环群时的相应结论.

英文摘要：

In this article,we study the problem of the structure classification of the Hopf algebra.By using the module category and the quiver,we obtain the distinct isomorphic classification of Hopf path coalgebras kG~c and the structure of Hopf subalgebra of kG[kQ_1],when G is a dihedral group D_2,that is,an abelian group of degree 4.This conclusion extends the results when G is a cyclic group of degree 2.