交换群上Hopf路余代数的结构分类 |
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引用本文: | 吴美云. 交换群上Hopf路余代数的结构分类[J]. 数学物理学报(A辑), 2009, 29(4): 1119-1131 |
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作者姓名: | 吴美云 |
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作者单位: | 南通大学理学院,江苏南通,226007 |
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摘 要: | 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kZu(C) -模的直积范畴∏C∈K(G) MkZu(C)与kG-Hopf双模范畴kGkG MkGkG之间的同构, 可由u(C)(kQ1)1上的右kZu(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kQc的同构分类及其子Hopf代数kG[kQ1]结构.
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关 键 词: | Hopf代数 模 分歧 |
收稿时间: | 2007-11-20 |
修稿时间: | 2009-04-07 |
Structure Classification of Hopf Path Coalgebras over Abelian Groups |
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Affiliation: | (Department of Mathematics, Nantong University, Jiangsu Nantong 226007) |
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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 kGkG MkGkG isequivalent to the direct category ∏C ∈ K(G) MkZu(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 kQc in case G is a cyclic group and G is a Klein quaternion group, respectively. |
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Keywords: | Hopf algebrazz Modulezz Ramificationzz |
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