Linear transformations that preserve the Nilpotent matrices

Abstract

Let sln be the algebra of n × n matrices with zero trace and entries in a field with at least n elements. Let R be the set of nilpotent matrices. The main result in this paper is that the group of nonsingular linear transformations L on sln such that L(R) = R is generated by the inner automorphisms: X → S-1XS; the maps: X → aX, for a ≠ 0; and the map: X → Xt that sends a matrix X to its transpose. © 1983 by Pacific Journal of Mathematics.