Vol. 92, No. 2, 1981

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ISSN: 0030-8730
Maps on simple algebras preserving zero products. II. Lie algebras of linear type

Warren James Wong

Vol. 92 (1981), No. 2, 469–488
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

[x,y] = 0 =⇒ [f(x),f(y)] = 0,

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
Authors
Warren James Wong