A classification of nilpotent compatible Lie algebras

2024/06/06 by M. Ladra, Ladra, Manuel, Bernardo Leite da Cunha +3 · 1 citation
Mathematics · #Advanced Topics in Algebra #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.2406.04036

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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