Maps on simple algebras preserving zero products. II: Lie algebras of linear type

Abstract

The study of maps on an algebra which preserve zero products is suggested by recent studies on linear transformations of various types on the space of n × n matrices over a field, particularly Watkins work on maps preservingcommuting pairs of matrices. This article generalizes the result of Watkins by determining the bijective semilinear mapsf ona Lie algebra L with the property that. where x, y ∈ L, for a class of Lie algebras constructed from finite-dimensional simple associative algebras . © 1981, University of California, Berkeley. All Rights Reserved.