Solvable compatible Lie algebras with a given nilradical
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866918360116101120 |
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| author | Ouaridi, A. Fernández Navarro, R. M. Omirov, B. A. Solijanova, G. O. |
| author_facet | Ouaridi, A. Fernández Navarro, R. M. Omirov, B. A. Solijanova, G. O. |
| contents | We extend the classical construction of solvable Lie algebras from a nilradical to compatible Lie algebras. Since the sum of nilpotent ideals may fail to be nilpotent, we replace the usual nilradical by a \emph{special nilradical} that behaves well with the mixed Jacobi identity. We use the maximal tori of diagonal derivations to build solvable extensions. The method is applied to the pairs $(\mathrm L_n,\mathrm R_n)$ and $(\mathrm L_n,\mathrm W_n)$, yielding explicit one-dimensional solvable extensions and proving nonexistence of higher-dimensional ones in these cases. We also study filiform compatible Lie algebras. We introduce the model family $\mathcal L_s$ and show that each $\mathcal L_s$ is a linear deformation of the model filiform Lie algebra $\mathcal L_k$. Finally, we study the existence of solvable extensions of this family, within the framework developed above. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_24094 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Solvable compatible Lie algebras with a given nilradical Ouaridi, A. Fernández Navarro, R. M. Omirov, B. A. Solijanova, G. O. Rings and Algebras 17A30, 17B30, 17B40, 17B56 We extend the classical construction of solvable Lie algebras from a nilradical to compatible Lie algebras. Since the sum of nilpotent ideals may fail to be nilpotent, we replace the usual nilradical by a \emph{special nilradical} that behaves well with the mixed Jacobi identity. We use the maximal tori of diagonal derivations to build solvable extensions. The method is applied to the pairs $(\mathrm L_n,\mathrm R_n)$ and $(\mathrm L_n,\mathrm W_n)$, yielding explicit one-dimensional solvable extensions and proving nonexistence of higher-dimensional ones in these cases. We also study filiform compatible Lie algebras. We introduce the model family $\mathcal L_s$ and show that each $\mathcal L_s$ is a linear deformation of the model filiform Lie algebra $\mathcal L_k$. Finally, we study the existence of solvable extensions of this family, within the framework developed above. |
| title | Solvable compatible Lie algebras with a given nilradical |
| topic | Rings and Algebras 17A30, 17B30, 17B40, 17B56 |
| url | https://arxiv.org/abs/2602.24094 |