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[1] Wang Shengxiang, Zhou Jianhua,. Crossed modules of Lie color algebras [J]. Journal of Southeast University (English Edition), 2012, 28 (4): 502-504. [doi:10.3969/j.issn.1003-7985.2012.04.023]
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Crossed modules of Lie color algebras()
李着色代数的交叉模
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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
28
Issue:
2012 4
Page:
502-504
Research Field:
Mathematics, Physics, Mechanics
Publishing date:
2012-12-30

Info

Title:
Crossed modules of Lie color algebras
李着色代数的交叉模
Author(s):
Wang Shengxiang1;  2;  Zhou Jianhua1
1 Department of Mathematics, Southeast University, Nanjing 211189, China
2School of Mathematics Sciences, Chuzhou University, Chuzhou 239000, China
王圣祥1;  2;  周建华1
1东南大学数学系, 南京 211189; 2滁州学院数学科学学院, 滁州 239000
Keywords:
crossed modules of Lie color algebras;  Witt type Lie color algebra;  third cohomology;  isomorphism
李着色代数的交叉模;  Witt型李着色代数;  三阶上同调;  同构
PACS:
O153.5
DOI:
10.3969/j.issn.1003-7985.2012.04.023
Abstract:
The linear operations of the equivalent classes of crossed modules of Lie color algebras are studied. The set of the equivalent classes of crossed modules is proved to be a vector space, which is isomorphic with the homogeneous components of degree zero of the third cohomology group of Lie color algebras. As an application of this theory, the crossed modules of Witt type Lie color algebras is described, and the result is proved that there is only one equivalent class of the crossed modules of Witt type Lie color algebras when the abelian group Γ is equal to Γ+. Finally, for a Witt type Lie color algebra, the classification of its crossed modules is obtained by the isomorphism between the third cohomology group and the crossed modules.
研究了李着色代数的交叉模等价类集合中的线性运算.证明了交叉模的等价类集合是一个线性空间, 而且它与李着色代数的三阶上同调的零次齐次部分空间同构.作为这个理论的一个应用, 刻画了Witt型李着色代数的交叉模, 当交换群Γ等于Γ+时, 证明了Witt型李着色代数的交叉模等价类只有一个.最后, 根据三阶上同调与交叉模之间的同构关系, 对Witt型李着色代数的交叉模进行了分类.

References:

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[2] Majid S. Algebras and Hopf algebras in braided categories[J]. Marcel Dekker Lecture Notes in Mathematics, 1994, 158(1):55-105.
[3] Scheunert M, Zhang N B. Cohomology of Lie superalgebras and their generalizations[J]. J Math Phys, 1998, 39(9):5024-5061.
[4] Pei F, Zhou J H. Crossed modules for Lie color algebras [J]. Journal of Southeast University: Natural Science Edition, 2007, 37(6):1137-1140.(in Chinese)
[5] Wang S X, Zhou J H. Crossed modules of Lie algebras [J]. Journal of Southeast University: Natural Science Edition, 2009, 39(1):185-190.(in Chinese)
[6] Kassel C, Loday J L. Extensions centrales d’algèbres de Lie[J]. Ann Inst Fourier, 1982, 32(4):119-142.
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Memo

Memo:
Biographies: Wang Shengxiang(1979—), male, graduate; Zhou Jianhua(corresponding author), male, doctor, professor, jhzhou@seu.edu.cn.
Foundation items: The Natural Science Foundation of Jiangsu Province(No.BK2012736), the Natural Science Foundation of Chuzhou University(No.2010kj006Z).
Citation: Wang Shengxiang, Zhou Jianhua. Crossed modules of Lie color algebras[J].Journal of Southeast University(English Edition), 2012, 28(4):502-504.[doi:10.3969/j.issn.1003-7985.2012.04.023]
Last Update: 2012-12-20