| 代数的交叉模 |
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| 引用本文： | 裴凤,周建华. 代数的交叉模[J]. 东南大学学报(自然科学版), 2007, 37(6): 1137-1140 |
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| 作者姓名： | 裴凤 周建华 |
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| 作者单位： | 东南大学理学院,南京,210096;合肥工业大学管理学院,合肥,230009;东南大学理学院,南京,210096 |
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| 摘 要： | 在李代数交叉模概念的基础上,提出了Lie color代数交叉模的概念.对给定的Lie color代数L,P以及阶化P-模M,考虑L的所有以M为核、以P为余核的交叉模,在这些交叉模之间定义了一个等价关系,证明了等价类集CML(P,L;M)与三阶上同调群H3(P,L;M)的零次齐次部分之间存在一一对应,从而可以利用三维上同调群对Lie color代数的交叉模进行分类.
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| 关 键 词： | Lie color代数 交叉模 上同调 一一对应 |
| 文章编号： | 1001-0505(2007)06-1137-04 |
| 修稿时间： | 2007-04-16 |
Crossed modules for Lie color algebras |
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| Pei Feng,Zhou Jianhua. Crossed modules for Lie color algebras[J]. Journal of Southeast University(Natural Science Edition), 2007, 37(6): 1137-1140 |
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| Authors: | Pei Feng Zhou Jianhua |
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| Abstract: | The notion of crossed modules for Lie color algebras is introduced.Let L and P be Lie color algebras and let M be a graded module over P,the crossed modules which make M as their kerneland P cokernel are considered.It is shown that under a suitable equivalent relation,there is a bijection between the set of the equivalent classes CML(P,L;M) and the homogeneous components of degree zero of H3(P,L;M). |
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| Keywords: | Lie color algebras crossed modules cohomology bijection |
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