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arXiv · 2407.11757

Leibniz algebras with an abelian subalgebra of codimension tw0

A. Fernandez Ouaridi·D. A. Towers
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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 $\mathfrak{h}(\mathbb{F}) \oplus \mathbb{F}^{n-4}$.

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A. Fernandez Ouaridi, D. A. Towers. 2024-07-16. Leibniz algebras with an abelian subalgebra of codimension tw0. https://arxiv.org/abs/2407.11757

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