具正规化子条件的Lie代数

Lie Algebras with the Normalizing Condition

给出具正规化子条件的Lie代数及Lie代数的次理想两个概念,讨论了它们的一些性质及其相互关系,证明了特征数零域F上有限维Lie代数为具正规化子条件的Lie代数当且仅当它是幂零的。

In this paper, Lie Algebras with the normalizing condition and the subnormal ideals of Lie Algebras will be definitions,Some propositions of them and their relations are discussed. It has been obtained a sufficient and neccessary condition for a finite dimensional Lie Algebra over a field of characteristic 0 with the normalizing condition.