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

Abstract

For a natural number $m$, a Lie algebra $L$ over a field $k$ is said to be of breadth type $(0,m)$ if the co-dimension of the centralizer of every non-central element is of dimension $m$. In this article, we classify finite dimensional nilpotent Lie algebras of breadth type $(0,3)$ over ${\mathbb{F}}_q$ of odd characteristics up to isomorphism. We also give a partial classification of the same over finite fields of even characteristic, $\mathbb{C}$ and $\mathbb{R}$. We also discuss $2$-step nilpotent Camina Lie algebras.

24 pages

References in corpus (1)

• Finite $p$-groups of conjugate type $\{1,p^3\}$

Cited by in corpus (1)

• Nilpotent Lie algebras with two centralizer dimensions over a finite field