Automorphisms of the Lie algebra of strictly upper triangular matrices over a commutative ring Original Research Article

Let R be an arbitrary commutative ring with identity. Denote by n(R) the Lie algebra over R consisting of all strictly upper triangular (n+1)×(n+1) matrices over R with ngreater-or-equal, slanted3. In addition, for n=3 assume that the annihilator of 2 in R is zero. The aim of this paper is to describe the automorphism group of n(R). We show that any automorphism phi of n(R) can be expressed as phi=ω·ξ·μ·σ where ω,ξ,μ and σ are graph, extremal, central and inner automorphisms, respectively, of n(R).