一类n维李三系的分类  

One kind of classifications of n-dimensional Lie triple systems

作　　者：尹建华[1] 徐琳[1] 汪云芬[1] 

机构地区：[1]承德民族师范高等专科学校数学系,河北承德067000

出　　处：《辽宁师范大学学报（自然科学版）》2007年第4期414-417,共4页Journal of Liaoning Normal University:Natural Science Edition

摘　　要：李三系是李代数三元运算的自然推广.主要讨论了复数域上一类n维李三系的分类,设T是一个带有三元运算[x,y,z]=f(y,z)x-f(x,z)y的n维李三系,其中f是T上的对称双线性函数,利用对称双线性函数的标准型,得到所有此类n维李三系的分类,即可分为n+1类.然后讨论了这类李三系的关于单纯,可解,Abel性质.The concept of Lie triple system is a natural generalization of the ternary operation of Lie algebra. In this paper, we classify a class of n-dimensional Lie triple systems over the complex number field. We let T be a n-dimensional Lie triple system with the ternary operation [x,y,z]=f（y,z）x-f （x,z）y, where f（x,y） is a symmetric bilinear function. We have got the classification for all the n-dimensional Lie triple systems through the use of the standard form of the symmetric bilinear functions, i.e. They can be classified into n＋1 types. We also make a discussion about the simple, solvable, and Abel properties of Lie triple systems.

关 键 词：李三系 理想 可解 对称双线性函数 

分 类 号：O152.5[理学—数学]