具有1-维导代数的6-维3-李代数的结构(英文)  

Structures of six-Dim 3-Lie algebras with one-Dim derived algebras

作　　者：白瑞蒲[1] 陈双双[1] 程荣[1] 李奇勇[1] 

机构地区：[1]河北大学数学与计算机科学学院,保定071002

出　　处：《黑龙江大学自然科学学报》2013年第4期421-424,共4页Journal of Natural Science of Heilongjiang University

基　　金：The Natural Science Foundation of Hebei Province(A2010000194);Foundation of Graduate Education Reform of Hebei University(YJ11-25,YJ11-07)

摘　　要：3-李代数与数学及数学物理的很多领域有着密切的关系。研究6-维3-李代数的结构,对特征零域上导代数维数为1的6-维3-李代数L,研究L的内导子代数adL的结构及导子代数DerL的结构,给出每个内导子及导子的具体表达形式。讨论导代数维数为1的6-维3-李代数L的度量结构,证明特征零域上导代数维数为1的6-维3-李代数L不存在度量函数。3 -Lie algebras have close relationships with the fields of mathematics and mathematical physics. Structures of six - dimensional 3 - Lie algebras are considered. For the six-dimensional 3 - Lie algebras L with dimL1 = 1 over a field of characteristic zero, the inner derivation algebras adL and deriva- tion algebras DerL are studied, and every derivation and inner derivation are provided concretely. The metric structures of the six-dimensional 3 - Lie algebras L with dimL1 = 1 are discussed, and it is proved that there does not exist metric structure on L.

关 键 词：3-李代数 内导子 导子 度量 

分 类 号：O189.1[理学—数学]