Department of Mathematics, Xiangtan University, Xiangtan, Hunan 411105, People's Republic of China
Abstract:
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 n3 a linear map on N(F) preserves commutativity in both directions if and only if =′+f where ′ is a product of standard maps on N(F) and f is a linear map of N(F) into its center.