n-RDS型李代数及其构造

On n－RDS Type Lie Algebras and Their Construction

本文通过对李代数理想格的讨论，研究李代数的结构。根据理想格满足的一些条件，给出李代数的一簇子类Rn，n≥1，Rn中元素称为n－RDS型李代数。本文刻划了Rn的一些特性，并得到了关于特征零代数闭域F上有限维n－RDS型李代数的一系列结果，特别是，对n≥2决定了所有n－RDS型李代数；证明了：对任何正整数N，存在N维可解1－RDS型李代数。

The structure of a Lie algebra is discussed by looking into the lattice of its ideals． From this point of view， a class of Lie algebras，called n－ RDS type Lie algebras， is introduced．A series of results are obtained when the base field is characteristic zero and algebraically closed．Particularly，in the case of n≥2，all the n－RDS type Lie algebras are constructed． Also the existence theorem of solvable RDS type Lie algebras is presented．