有限维单李代数的伴随表示分解

Adjoint representation decomposition of finite dimensional simple Lie algebras

利用有限维单李代数根空间分解,给出复数域上有限维单李代数的根链;利用复数域上不可约sl(2,C)-模的分类,给出有限维单李代数g在伴随作用下分解成g的不可约sl(2,C)-子模直和的分解式.

In this paper,the root chain of finite dimensional simple Lie algebras over complex field is given by means of the root space decomposition of finite dimensional simple Lie algebras.By usingthe classification of irreducible sl(2,C)-modules over complex field,finite dimensional simple Lie algebras g over complex field under adjoint action as sl(2,C)-module is decomposed into a direct sum of irreducible submodule of g.