Commutativity preserving linear maps and Lie automorphisms of strictly triangular matrix space

Abstract

AbstractIn this paper we classify linear maps preserving commutativity in both directions on the space N(F) of strictly upper triangular (n+1)×(n+1) matrices over a field F. We show that for n⩾3 a linear map ϕ on N(F) preserves commutativity in both directions if and only if ϕ=ϕ′+f where ϕ′ is a product of standard maps on N(F) and f is a linear map of N(F) into its center