Crossed modules of Lie color algebras  

李着色代数的交叉模(英文)

作　　者：王圣祥[1,2] 周建华[1] 

机构地区：[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

出　　处：《Journal of Southeast University(English Edition)》2012年第4期502-504,共3页东南大学学报（英文版）

基　　金：The Natural Science Foundation of Jiangsu Province(No.BK2012736);the Natural Science Foundation of Chuzhou University(No.2010kj006Z)

摘　　要：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 Г is equal to Г＋. 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.

关 键 词：crossed modules of Lie color algebras Witt type Lie color algebra third cohomology ISOMORPHISM 

分 类 号：O153.5[理学—数学]