A classification of nilpotent compatible Lie algebras
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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 one 2-parameter family in dimension 4.
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Ladra, 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-z
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https://doi.org/10.1007/s12215-024-01126-zSponsors
Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. The first and second authors are supported by Agencia Estatal de Investigación (Spain), grant PID2020-115155GB-I00 (European FEDER support included, UE) and by Xunta de Galicia through the Competitive Reference Groups (GRC), ED431C 2023/31. The second author is supported by an FCT—Fundação para a Ciência e a Tecnologia, I.P scholarship with reference number 2023.00796.BD. The second and third authors are supported by CMUP, a member of LASI, which is financed by national funds through FCT—Fundação para a Ciência e a Tecnologia, I.P., under the projects with reference UIDB/00144/2020 and UIDP/00144/2020.
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© 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.