关于李代数导子的若干性质

SOME PROPERTIES OF THE DERIVATIONS OF LIE ALGEBRAS

本文仅对特征为零的有限维李代数作探讨。首先以一个例子来指明Zassenhaus的逆定理是不成立的。然后引入导子理想、可解导子理想以及导子单代数的概念。用这些工具,得到了一些结果,主要的是命题10L_D=R与命题12,后者是半单李代数的一个结构定理。

In this paper we shall consider only finite dimensional Lie algebras of characteristic zero. At first we give an example to illustrate the falsity of the converse theorem of Zassenhaus.Then we introduce the conceptions of derivation-ideals,solvable derivation-ideals and simple derivation-algebras. By using these tools, the main results we obtained are Proqp 10LD=R and Prop. 12, the structure theorem of semisimple Lie algebras.