Vol. 104, No. 1, 1983

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ISSN: 0030-8730
Linear transformations that preserve the nilpotent matrices

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

Vol. 104 (1983), No. 1, 39–46

Let sln 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 sln such that L(N) = N is generated by the inner automorphisms: X S1XS; the maps: X aX, for a0; and the map: X Xt that sends a matrix X to its transpose.

Mathematical Subject Classification 2000
Primary: 15A23
Secondary: 20G15
Received: 16 March 1979
Revised: 28 December 1980
Published: 1 January 1983
Peter Botta
Stephen J. Pierce
William E. Watkins