交换群上Hopf路余代数的结构分类

Abstract

Abstract:

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_kGM^kG_kGis

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^cand 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.

Key words: Hopf algebra, Module, Ramification

CLC Number:

16w30

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WU Mei-Yun. Structure Classification of Hopf Path Coalgebras over Abelian Groups[J].Acta mathematica scientia,Series A, 2009, 29(4): 1119-1131.

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Structure Classification of Hopf Path Coalgebras over Abelian Groups

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