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

In this article we classify linear maps phi from the algebra image of n × ? upper triangular matrices into itself satisfying phi(ab − ba) = 0 if and only if ab − BA = 0. In particular, we show that for n> 2, any such map is either the sum of an algebra automorphism and a map into the centre, or the sum of the negative of an algebra anti-automorphism and a map into the centre. As a consequence, Lie automorphisms of the algebra image are also classified.