一类链条件Lie代数的结构

The Structures of a Class of Lie Algebras with Chain Conditions

有限维完备Lie代数的结构(分解唯一性)及链条件Lie代数的结构是很清楚的。本文将这些定理及所用方法推广到中心是零的链条件Lie代数(维数不一定有限)的情形,使这一类Lie代数的结构更加完美。

The structures of finite dimensional complete Lie algebras and of Lie algebras with chain coditions are clear. The main object of this paper is to extend the method used above to the case of Lie algebras with centre zero and chain conditions .So we get more perfect results of this class of Lie algebras.