Commutativity preserving linear maps and Lie automorphisms of triangular matrix algebras

In this article we classify linear maps phi from the algebra T-n of n x n u pper triangular matrices into itself satisfying phi(ab - ba) = 0 if and onl y if ab - ba = 0. In particular, we show that for n > 2, any such map is ei ther the sum of an algebra automorphism and a map into the centre, or the s um of the negative of an algebra anti-automorphism and a map into the centr e. As a consequence, Lie automorphisms of the algebra T-n are also classifi ed. (C) 1999 Elsevier Science Inc. All rights reserved.