Nilpotent Lie algebras with two centralizer dimensions over a finite field

Rijubrata Kundu; Tushar Kanta Naik; Anupam Singh

doi:10.1016/j.jalgebra.2023.06.013

paper

Nilpotent Lie algebras with two centralizer dimensions over a finite field

arXiv:2208.07676 · doi:10.1016/j.jalgebra.2023.06.013

Abstract

A result of Barnea and Isaacs states that if $L$ is a finite dimensional nilpotent Lie algebra with exactly two distinct centralizer dimensions, then nilpotency class of $L$ is either $2$ or $3$ . In this article, we classify all such finite dimensional $3$ -step nilpotent Lie algebras over a finite field.

References in corpus (1)

Nilpotent Lie Algebras of breadth type $(0, 3)$