[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]
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李代数的交叉模()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
39
期数:
2009年第1期
页码:
185-190
栏目:
数学、物理学、力学
出版日期:
2009-01-20

文章信息/Info

Title:
Crossed modules of Lie algebras
作者:
王圣祥1 周建华2
1 滁州学院数学系, 滁州 239000; 2 东南大学理学院, 南京 210096
Author(s):
Wang Shengxiang1 Zhou Jianhua2
1 Department of Mathematics, Chuzhou University, Chuzhou 239000, China
2 School of Science, Southeast University, Nanjing 210096, China
关键词:
李代数的交叉模 三阶上同调群 Virasoro 代数 同构 等价
Keywords:
crossed modules of Lie algebras third cohomology Virasoro algebra isomorphism equivalence
分类号:
153.5
DOI:
10.3969/j.issn.1001-0505.2009.01.036
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,PP-M,考虑所有以M为核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间,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.
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:

[1] Kassel C,Loday J L.Extensions centrales d,alg’ebres de Lie[J]. Ann Inst Fourier(Grenoble),1982,32(4):119-142.
[2] 裴凤,周建华.Lie color代数的交叉模[J].东南大学学报:自然科学版,2007,37(6):1137-1140.
  Pei Feng,Zhou Jianhua.Crossed modules for Lie color algebras[J].Journal of Southeast University:Natural Science Edition,2007,37(6):1137-1140.(in Chinese)
[3] Wagemann F.A crossed modules representing the Godbillon-Vey cocycle [J]. Letters in Mathematical Physics,2000,51(4):293-299.
[4] Wagemann F.On Lie algebra crossed modules [J]. Comm Alg,2006,34(5):1699-1722.
[5] Zhang Hechun.A class of representative over the Virasoro algebras [J]. J Alg,1997,190:1-10.
[6] Rupet Wei Tze Yu.Algebras de Lie de type Witt [J].Comm Alg, 1997,25(5):1471-1484.

备注/Memo

备注/Memo:
作者简介: 王圣祥(1979—),男,硕士,讲师,wangsx-math@163.com.
引文格式: 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.
更新日期/Last Update: 2009-01-20