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

In 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 ngreater-or-equal, slanted3 a linear map phi on N(F) preserves commutativity in both directions if and only if phi=phi′+f where phi′ is a product of standard maps on N(F) and f is a linear map of N(F) into its center.