算子李代数的一些性质  

Some Results of Operator Lie Algebras

作　　者：姜玉秋[1] 

机构地区：[1]吉林师范大学数学学院,吉林四平136000

出　　处：《数学的实践与认识》2009年第3期188-193,共6页Mathematics in Practice and Theory

基　　金：国家自然科学基金项目(10626011)

摘　　要：算子群作为群的推广,算子群在群论里有许多应用.类似地,作为算子群和李代数的推广,算子李代数将会有许多应用.给出了算子李代数的一些性质,得到了算子李代数半单性的充分必要条件.同时得到算子李代数半单性与非退化killing型的关系.Operator groups as a generalization of groups is well delveloped and has proved useful in the study of certain typies of problem in group theory. The purpose of present paper is to develop operator groups for operator Lie algebras. Some important properties of operator Lie algebras are given, and some necessary and sufficient conditions on semisimple operator Lie algebras are obtained. Moreover, the relationships between semisimple operator Lie algebras and nondegenerate killing form of operator Lie algebras are concerned.

关 键 词：李代数 算子李代数 KILLING型 

分 类 号：O152.5[理学—数学]