# [1]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):185-190.[doi:10.3969/j.issn.1001-0505.2009.01.036] 　Wang Shengxiang,Zhou Jianhua.Crossed modules of Lie algebras[J].Journal of Southeast University (Natural Science Edition),2009,39(1):185-190.[doi:10.3969/j.issn.1001-0505.2009.01.036] 点击复制 李代数的交叉模() 分享到： var jiathis_config = { data_track_clickback: true };

39

2009年第1期

185-190

2009-01-20

## 文章信息/Info

Title:
Crossed modules of Lie algebras

1 滁州学院数学系, 滁州 239000; 2 东南大学理学院, 南京 210096
Author(s):
1 Department of Mathematics, Chuzhou University, Chuzhou 239000, China
2 School of Science, Southeast University, Nanjing 210096, China

Keywords:

153.5
DOI:
10.3969/j.issn.1001-0505.2009.01.036

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 isomorphic with its third cohomology. Finally, the third cohomology of Virasoro algebra is calculated.

## 参考文献/References:

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