一类李代数的结构

The Structure of a Kind of Lie Algebra

本文给出了复数域Ｃ上具有有限多个理想的有限维非可解李代数的结构为Ｌ＝Ｃｒ○＋Ｎ○＋Ｓ，其中Ｓ是Ｌ的Ｌｅｖｉ因子，Ｎ是Ｌ的幂零根基，Ｃｒ○＋Ｎ是Ｌ的根基，ａｄｒ是Ｎ的半单纯线性变换，［ｒ，Ｓ］＝０；还给出了这类李代数的一些重要性质．

Let L be a finite dimensional unsovable Lie algebra with finite number of ideals over the complex number field C. The paper obtained the structure and some important properties ofL. In addition, we give the sufficient and necessary condition underwhich a nilpotent Lie algebra has finite number of ideals.