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arXiv · 2602.24094

Solvable compatible Lie algebras with a given nilradical

A. Fernández Ouaridi·R. M. Navarro·B. A. Omirov·G. O. Solijanova
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Abstract

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.

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A. Fernández Ouaridi, R. M. Navarro, B. A. Omirov, G. O. Solijanova. 2026-02-27. Solvable compatible Lie algebras with a given nilradical. https://arxiv.org/abs/2602.24094

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