Ladra González, ManuelLeite da Cunha, BernardoLopes, Samuel A.2025-06-192025-06-192025-01-22Ladra, M., Leite da Cunha, B. & Lopes, S.A. A classification of nilpotent compatible Lie algebras. Rend. Circ. Mat. Palermo, II. Ser 74, 70 (2025). https://doi.org/10.1007/s12215-024-01126-z0009-725Xhttps://hdl.handle.net/10347/42177Working 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 one 2-parameter family in dimension 4.eng© TheAuthor(s) 2024 Attribution 4.0 International. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.http://creativecommons.org/licenses/by/4.0/Algebraic GeometryAssociative Rings and AlgebrasCommutative Rings and AlgebrasMultilinear AlgebraTopological Groups and Lie GroupsGroup Theory and Generalizationsjournal article10.1007/s12215-024-01126-zopen access