一类无限维完备李代数的2-局部齐次导子  

The 2-local Homogeneous Derivations of a Class of Infinite Dimensional Complete Lie Algebras

作　　者：黄杰 王宪栋 Jie HUANG;Xian Dong WANG(School of Construction and Environmental Engineering,Dongying Vocational Institute,Dongying 257091,P.R.China;School of Mathematics and Statistics,Qingdao University,Qingdao 266101,P.R.China)

机构地区：[1]东营职业学院建筑与环境工程学院,东营257091 [2]青岛大学数学与统计学院,青岛266101

出　　处：《数学学报（中文版）》2022年第5期951-958,共8页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11472144)。

摘　　要：通过对复数域上单李代数的Loop代数进行一维导子扩张,得到一类无限维完备李代数;利用其根空间分解及无外导子的性质,证明了这类无限维完备李代数的2-局部齐次导子都是导子.In this paper,a class of infinite dimensional complete Lie algebras is obtained by extending the one dimensional homogeneous derivations of Loop algebras over simple Lie algebras.It is proved that every 2-local homogeneous derivation of this kind of infinite dimensional complete Lie algebra is a derivation.

关 键 词：无限维完备李代数 根空间分解 导子 2-局部齐次导子 

分 类 号：O151.2[理学—数学]