Linear transformations that preserve the nilpotent matrices

Peter Botta, Stephen J. Pierce and William E. Watkins

Vol. 104 (1983), No. 1, 39–46

DOI: 10.2140/pjm.1983.104.39

Abstract

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

Mathematical Subject Classification 2000

Primary: 15A23

Secondary: 20G15

Milestones

Received: 16 March 1979

Revised: 28 December 1980

Published: 1 January 1983