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A classification of nilpotent compatible Lie algebras

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arxiv 2406.04036 v2 pith:22EZGCCM submitted 2024-06-06 math.RA

Manuel Ladra , Bernardo Leite da Cunha , Samuel A. Lopes This is my paper · ORCID
classification math.RA
keywords algebrascompatibledimensionclassesclassificationfamiliesfieldisomorphism
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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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Cited by 1 Pith paper

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  1. Compatible anti-pre-Lie algebras

    math.RA 2024-12 reject novelty 4.0 of 10

    Compatible anti-pre-Lie algebras are introduced, characterized via negative left multiplication representations, and classified in dimension 2 by a list of 45 families.

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