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arXiv · 2406.04036

A classification of nilpotent compatible Lie algebras

Manuel Ladra·Bernardo Leite da Cunha·Samuel A. Lopes
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Abstract

Working over an arbitrary field of characteristic different from $2$, we extend the Skjelbred-Sund method to compatible Lie algebras and give a full classification of nilpotent compatible Lie algebras up to dimension $4$. In case the base field is cubically closed, we find that there are three isomorphism classes and a one-parameter family in dimension $3$, and $12$ isomorphism classes, $6$ one-parameter families and two $2$-parameter families in dimension $4$

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Manuel Ladra, Bernardo Leite da Cunha, Samuel A. Lopes. 2024-06-06. A classification of nilpotent compatible Lie algebras. https://doi.org/10.1007/s12215-024-01126-z

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