Leibniz algebras with an abelian subalgebra of codimension tw0
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917723514077184 |
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| author | Ouaridi, A. Fernandez Towers, D. A. |
| author_facet | Ouaridi, A. Fernandez Towers, D. A. |
| contents | 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 $\mathfrak{h}(\mathbb{F}) \oplus \mathbb{F}^{n-4}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_11757 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Leibniz algebras with an abelian subalgebra of codimension tw0 Ouaridi, A. Fernandez Towers, D. A. Rings and Algebras Group Theory 17A32, 17B05, 17B20, 17B30 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 $\mathfrak{h}(\mathbb{F}) \oplus \mathbb{F}^{n-4}$. |
| title | Leibniz algebras with an abelian subalgebra of codimension tw0 |
| topic | Rings and Algebras Group Theory 17A32, 17B05, 17B20, 17B30 |
| url | https://arxiv.org/abs/2407.11757 |