1. On the nilpotent commutator of a nilpotent matrix.
- Author
-
Oblak, Polona
- Subjects
- *
COMMUTATORS (Operator theory) , *NILPOTENT groups , *MATRICES (Mathematics) , *ORBIT method , *GROUP theory , *MATHEMATICAL analysis - Abstract
We study the structure of the nilpotent commutator 𝒩 B of a nilpotent matrix B. We show that 𝒩 B intersects all nilpotent orbits for conjugation if and only if B is a square-zero matrix. We describe nonempty intersections of 𝒩 B with nilpotent orbits in the case the n × n matrix B has rank n − 2. Moreover, we give some results concerning the inverse image of the map taking B to the maximal nilpotent orbit intersecting 𝒩 B . [ABSTRACT FROM AUTHOR]
- Published
- 2012
- Full Text
- View/download PDF