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

Abstract

LetRbe an arbitrary commutative ring with identity. Denote bytthe Lie algebra overRconsisting of all upper triangularnbynmatrices overRand letbbe the Lie subalgebra oftconsisting of all matrices of trace 0. The aim of this paper is to give an explicit description of the automorphism group of the Lie algebrat, which extends a result given by Doković. In addition, we explicitly describe the automorphism group of the Lie algebrabwhennis a unit ofR. © 1997 Academic Press.