关于李三系的分类  

On the Classification of Lie Triple Systems

作　　者：张知学[1] 潘淑杰[2] 刘文丽[1] 

机构地区：[1]河北大学数学与计算机学院,河北保定071002 [2]山东理工大学数学与信息科学学院,山东淄博255000

出　　处：《数学年刊（A辑）》2008年第6期779-788,共10页Chinese Annals of Mathematics

基　　金：河北省自然科学基金(No．A2005000088)资助的项目．

摘　　要：首先基于复单李代数的所有对合自同构的分类,研究了复单李三系的分类.然后研究了实单李三系的分类,得到了实单李三系或者同构于一个复单李三系的实形式,或者同构于复单李三系的实化的结论.同时还给出了关于实李三系复化和复李三系实化的部分结果.This paper investigates the classification of complex simple Lie triple systems based on the classification of all involution automorphisms for each complex simple Lie algebra using Kac＇s method. Then the authors study the classification of real simple Lie triple systems and show that a real simple Lie triple system is either isomorphic to a real form of a complex simple Lie triple system or to the realification of a complex simple Lie triple system. At the same time some results about the complexification of a real Lie triple system and the realification of a complex Lie triple system are given.

关 键 词：李三系 标准嵌入李代数 对合 复化 实化 

分 类 号：O152.5[理学—数学]