| 李代数的交叉模 |
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| 引用本文： | 王圣祥,周建华.李代数的交叉模[J].东南大学学报(自然科学版),2009,39(1). |
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| 作者姓名： | 王圣祥 周建华 |
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| 作者单位： | 1. 滁州学院数学系,滁州,239000
2. 东南大学理学院,南京,210096 |
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| 摘 要： | 介绍了李代数交叉模的一个等价定义,用等价定义讨论了交叉模等价类之间的运算.对给定的李代数L,P及P.模M,考虑所有以M为核、以P为余核的交叉模的等价类集合,在等价类集中定义加法运算和数乘运算.证明了李代数的交叉模等价类集合是一个线性空闸,且与其三阶上同调群空间同构.最后计算了Virasoro代数的三阶上同调群.
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| 关 键 词： | 李代数的交叉模 三阶上同调群 Virasoro代数 同构 等价 |
Crossed modules of Lie algebras |
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| Wang Shengxiang,Zhou Jianhua.Crossed modules of Lie algebras[J].Journal of Southeast University(Natural Science Edition),2009,39(1). |
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| Authors: | Wang Shengxiang Zhou Jianhua |
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| Institution: | 1Department of Mathematics;Chuzhou University;Chuzhou 239000;China;2School of Science;Southeast University;Nanjing 210096;China |
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| Abstract: | The definition of crossed modules of Lie algebras is introduced,and the operations of equivalent classes of crossed modules are discussed on the base of the given equivalent definition.Let L and P be Lie algebras and let M be a P-module,the equivalent classes of crossed modules which make M as their kernel and P cokernel are considered,then the operations of addition and multiplication are discussed.It is proved that the set of the equivalent classes of crossed modules is a vector space,and that the set is ... |
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| Keywords: | crossed modules of Lie algebras third cohomology Virasoro algebra isomorphism equivalence |
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