A classification of nilpotent compatible Lie algebras
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.
Authors
- M. Ladra (ORCID: https://orcid.org/0000-0002-0543-4508)
- Samuel A. Lopes (ORCID: https://orcid.org/0000-0002-1292-0977)
- Bernardo Leite da Cunha (ORCID: https://orcid.org/0000-0002-5640-5926)
Institutions
- Universidade do Porto (PT)
- Universidade de Santiago de Compostela (ES)
Publication Details
- Journal
- Rendiconti del Circolo Matematico di Palermo Series 2
- Published
- 2025-01-22
- DOI
- https://doi.org/10.1007/s12215-024-01126-z
- Citations
- 2
- Primary Topic
- Advanced Topics in Algebra
- Type
- article
- Field-Weighted Citation Impact
- 10.76
Funders
- Xunta de Galicia
- Fundação para a Ciência e a Tecnologia
- Centro de Matemática Universidade do Porto
- Agencia Estatal de Investigación