有限维单李代数的伴随表示分解  

Adjoint representation decomposition of finite dimensional simple Lie algebras

作　　者：史彦青 陈杏 李立斌[1] SHI Yanqing;CHEN Xing;LI Libin(School of Mathematical Science,Yangzhou University,Yangzhou 225002,China)

机构地区：[1]扬州大学数学科学学院,江苏扬州225002

出　　处：《扬州大学学报（自然科学版）》2024年第3期71-73,78,共4页Journal of Yangzhou University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11871063)。

摘　　要：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.

关 键 词：单李代数 根空间 根系 伴随表示 

分 类 号：O152.5[理学—数学]