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

Warren James Wong

Vol. 92 (1981), No. 2, 469–488

DOI: 10.2140/pjm.1981.92.469

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 preserving commuting pairs of matrices. This article generalizes the result of Watkins by determining the bijective semilinear maps f on a Lie algebra L with the property that

where x,y ∈ L, for a class of Lie algebras constructed from finite-dimensional simple associative algebras.

Mathematical Subject Classification 2000

Primary: 15A04

Secondary: 17B60, 16A46

Milestones

Received: 13 April 1977

Revised: 17 December 1979

Published: 1 February 1981