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Linear transformations that preserve the nilpotent matrices

1983; Mathematical Sciences Publishers; Volume: 104; Issue: 1 Linguagem: Inglês

10.2140/pjm.1983.104.39

ISSN

1945-5844

Autores

Peter Botta, Stephen Pierce, William Watkins,

Tópico(s)

Finite Group Theory Research

Resumo

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.

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