一类6维3-李代数的结构  

Structures of a Class of 6-dimensional 3-Lie Algebras

作　　者：范素军[1] 刘东艳[1] 

机构地区：[1]河北医科大学基础医学院,河北石家庄050017

出　　处：《河北师范大学学报（自然科学版）》2014年第2期109-112,共4页Journal of Hebei Normal University：Natural Science

基　　金：河北省自然科学基金(A2010000194)

摘　　要：研究了特征为0的代数闭域上导代数维数为1的6维3-李代数的结构.对3-李代数的可解性、幂零性及内导子代数的结构进行了研究,给出了每个内导子的具体表达形式,且证明了特征为0的代数闭域上导代数维数为1的6维3-李代数上不存在度量结构.The paper studies the structure of 6-dimensional 3-Lie algebras with one-dimensional derived algebras over an algebraically closed field of characteristic zero. The solvability, nilpotency, and the struclures of inner derivation algebras are discussed, the concrete expression of any inner derivation is provided. It is also proved that there does not exist metric structures on the 6-dimensional 3-Lie algebras with one-dimensional derived algebras.

关 键 词：3-李代数 可解性 幂零性 内导子 度量3-李代数 

分 类 号：O152.5[理学—数学]