【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.更多还原

【Abstract】 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更多还原