Automorphisms of certain Lie algebras of upper triangular matrices over a commutative ring

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 over R 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 automorphism group of the Lie algebra t, which extends a result given by Dokovic. In addition, we explicitly describe the automorphism group of the Lie algebra b when n is a unit of R. (C) 1997 Academic Press.