可换环上一些上三角矩阵李代数的导子

摘要

Let R be an arbitrary commutative ring with identity. Denote by t the Lie algebra over R consisting of all upper triangular n by n matrices and let b be the Lie subalgebra of t consisting of all matrices of trace 0. The aim of this paper is to give an explicit description of the derivation algebras of the Lie algebras t and b, respectively.%设R是任意含单位元的可换环,t是R上n×n上三角矩阵组成的李代数,b是R上迹为零的n×n上三角矩阵组成的李代数.本文明确给出了t和b的导子代数.