二面体群上Hopf路余代数的结构分类

Classification of Hopf Path Coalgebras over Dihedral Group

从Hopf quiver出发,借助于右kZ_u(c)-模的直积范畴■ Mkz_(u(C))与kG-Hopf双模范畴kG/kG M kG/kG之间的同构,当G是二面体群D_3时,给出了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 group algebra over a field k. It is well known that the kG-Hopf bimodule category kG ^kGMkG^kG is equivalent, to the direct product category ∏C∈K（G） MkZu（C）. This paper discusses the isomorphic classication of Hopf path coalgebras kQ^c and the structures of Hopf subalgebrass of kG[kQ1] when G is a dihedral group D3.