Linear transformations that preserve the nilpotent matrices

Abstract

Let si " be the algebra of nX n matrices with zero trace and entries in a field with at least n elements.Let 91 be the set of nilpotent matrices.The main result in this paper is that the group of nonsingular linear transformations L on sl M such that L(9l) = 91 is generated by the inner automorphisms: X-*S~ιXS;the maps: X -> aX, for a ¥= 0; and the map: X -> X* that sends a matrix X to its transpose.