Vol. 104, No. 1, 1983

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
The Journal
Editorial Board
Special Issues
Submission Guidelines
Submission Form
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
Other MSP Journals
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