Automorphisms of the Lie algebra of strictly upper triangular matrices over certain commutative rings Original Research Article

Let n be the nilpotent Lie algebra consisting of all strictly upper triangular (n+1)×(n+1) matrices over a commutative ring R. In this paper, we discuss the automorphism group of n. We prove that any automorphism phi of n can be uniquely expressed as phi=ω·η·ξ·μ·σ, where ω, η, ξ, μ and σ are graph, diagonal, external, central and inner automorphisms, respectively, of n when ngreater-or-equal, slanted3 and R is a local ring that contains 2 as a unit or an integral domain of characteristic other than two. In the case n=2 we also prove that any automorphism of n can be expressed as a product of graph, diagonal, extremal and inner automorphisms for an arbitrary local ring R.