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

摘要

In this paper we classify linear maps preserving commutativity in both directions on the space N(F) of strictly upper triangular (n + 1) x (n + 1) matrices over a field F. We show that for n greater than or equal to 3 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. (C) 2002 Elsevier Science Inc. All rights reserved. [References: 16]