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Commutativity preserving linear maps and Lie automorphisms of strictly triangular matrix space
Authors:You'an Cao  Zhonghu Chen  Chong Huang
Institution:

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 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.
Keywords:Strictly upper triangular matrices  Linear maps  Lie automorphisms  Commutativity
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