Derivations of the Lie algebra of strictly upper triangular matrices over a commutative ring

Abstract

Let R be an arbitrary commutative ring with identity, gl( n, R) the general linear Lie algebra consisting of all n × n matrices over R, N( n, R) the subalgebra of gl( n, R) consisting of all strictly upper triangular ones. In this paper, we give an explicit description of any derivations of N( n, R).