交换环上严格上三角矩阵的广义李三导子

摘要

本文研究了交换环R上所有n×n严格上三角矩阵构成的李代数N(n,R)(n ≥ 5)上广义李三导子.利用矩阵技巧,证明了N(n,R)(n≥5)上任意广义李三导子为一李三导子与一位似映射的和.对于N(n,R)(n≥3)上广义李导子,得出类似结果.%In this article,we mainly study generalized Lie triple derivations for the Lie algebra N(n,R)(n ≥ 5) consisting of all n × n strictly upper triangular matrices over a commutative ring R.Using matrix technique,we prove that every generalized Lie triple derivation of N(n,R)(n ≥ 5) is the sum of a Lie triple derivation and a homothety.A similar result for generalized Lie derivations of N(n,R)(n ≥ 3) is also obtained.