三维李三系及其导子代数  

Three-dimensional Lie triple systems and their derivation algebras

作　　者：卢艳霞[1] 史会峰[1] 

机构地区：[1]华北电力大学数理学院,河北保定071003

出　　处：《华北电力大学学报（自然科学版）》2005年第4期110-112,共3页Journal of North China Electric Power University：Natural Science Edition

摘　　要：根据李三系的Levi分解定理和Yamaguti关于二维李三系的分类结果,证明了复数域上的三维李三系可以写成一个半单李三子系和它中心的直和。在此基础上,对复数域上的三维李三系进行了分类,详细给出了每类李三系的乘法表。利用三维李三系的分类结果,计算了每种类型的李三系的导子代数的结构。Based on the Levi theorem of Lie triple systems and the classification result of Yamaguti about two-dimensional Lie triple systems, it is concluded that a three-dimensional non-solvable Lie triple can be written as the direct plus of a two-dimensional simple subsystem and its center in a complex field. The three-dimensional Lie triple system is classified. The no-zero multiplication table of Lie triple system is presented. The derivation algebras are calculated. The matrix elements of derivation algebra are obtained.

关 键 词：李三系 导子代数 中心 可解的 乘法表 

分 类 号：O152.5[理学—数学]