一类单完备李代数  

A Class of Simple Complete Lie Algebras

作　　者：李军波[1] 法焕霞[1] 

机构地区：[1]常熟理工学院数学系,江苏常熟215500

出　　处：《数学年刊（A辑）》2009年第3期401-410,共10页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.10671027;No.10825101)资助的项目

摘　　要：确定了代数V_(a,b,c)的导子代数,其中V_(a,b,c)是由非交换代数C_(a,b,c)[X^(±1),Y^(±1),Z^(±1)]的所有内导子所张成的李代数,证明了导子代数V_(a,b,c)是由所有内导子和3个外导子D_(1,0,0),D_(0,1,0),D_(0,0,1)张成的,同时还给出了一类无限维的单完备李代数。The derivation algebra of the algebra Va,b,c is determined in this paper, where Va,b,c denotes the Lie algebra of inner derivations of the algebra Ca,b,c[X^±1, Y^±1, Z^±1]. It is proved that the Lie algebra of derivations of Va,b,c is spanned by the inner derivations and three outer derivations D1,0,0, D0,1,0 and D0,0,1. As a result, an infinite simple complete Lie algebra is presented.

关 键 词：导子代数 内导子 单完备李代数 

分 类 号：O152.5[理学—数学]