Towers, David and Ouaridi, Amir
(2024)
*Leibniz algebras with an abelian subalgebra of codimension two.*
Linear Algebra and its Applications.
ISSN 0024-3795

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## Abstract

A characterization of the finite-dimensional Leibniz algebras with an abelian subalgebra of codimension two over a field $\mathbb{F}$ of characteristic $p\neq2$ is given. In short, a finite-dimensional Leibniz algebra of dimension $n$ with an abelian subalgebra of codimension two is solvable and contains an abelian ideal of codimension at most two or it is a direct sum of a Lie one-dimensional solvable extension of the Heisenberg algebra $\mathfrak{h}(\mathbb{F})$ and $\mathbb{F}^{n-4}$ or a direct sum of a $3$-dimensional simple Lie algebra and $\mathbb{F}^{n-3}$ or a Leibniz one-dimensional solvable extension of the algebra $\mathfrak{h}(\mathbb{F}) \oplus \mathbb{F}^{n-4}$.