On the nilpotent commutator of a nilpotent matrix

2011/06/08 by Polona Oblak, Oblak, Polona
Computer Science · Engineering · Mathematics · #14L30 #15A21 #15A27 #FOS: Mathematics #Finite Group Theory Research #Matrix Theory and Algorithms #Rings and Algebras (math.RA) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1106.1545

openalex publication_date 2011/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the structure of the nilpotent commutator \nb of a nilpotent matrix B. We show that \nb intersects all nilpotent orbits for conjugation if and only if B is a square--zero matrix. We describe nonempty intersections of \nb with nilpotent orbits in the case the n × n matrix B has rank n-2. Moreover, we give some results on the maximal nilpotent orbit that \nb intersects nontrivially.

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