三维实李代数的分类  

Classification of three-dimensional real Lie algebra

作　　者：胡建华[1] 栗菲菲 刘静 HU Jianhua;LI Feifei;LIU Jing(College of Science,University of Shanghai for Science and Technology,Shanghai 200093,China)

机构地区：[1]上海理工大学理学院,上海200093

出　　处：《上海理工大学学报》2020年第3期220-223,共4页Journal of University of Shanghai For Science and Technology

基　　金：上海理工大学教师教学发展研究基金资助项目(LXYJY07)。

摘　　要：根据李代数的导代数的性质及同构条件完成三维实李代数的分类。当导代数维数为0和1时,由李括号运算的性质及基的变换可将李代数分为三类:L(3,0),L(3,-1),L(3,1)。当导代数维数为2和3时,根据内导子对应矩阵特征值的性质可将李代数分为五类:L(3,2,a),L(3,3),L(3,4,c),L(3,5),L(3,6)。The classification of three-dimensional real Lie algebra was completed according to the properties of derivative algebras and isomorphic conditions of Lie algebra.When the dimension of derivative algebra is 0 or 1,Lie algebra can be divided into three types,(3,0),L(3,-1)and L(3,1),according to the properties of Lie bracket operation and the transformation of basis.When the dimension of derivative algebra is 2 or 3,Lie algebras can be divided into five types,L(3,2,a),L(3,3),L(3,4,c),L(3,5),L(3,6),according to the properties of eigenvalues of matrix corresponding to internal derivations.

关 键 词：李代数 导代数 同构 

分 类 号：O152[理学—数学]