A classification of nilpotent compatible Lie algebras

Manuel Ladra; Bernardo Leite da Cunha; Samuel A. Lopes

A classification of nilpotent compatible Lie algebras

Rings and Algebras 2024-11-11 v2

Authors: Manuel Ladra , Bernardo Leite da Cunha , Samuel A. Lopes

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 $4$

Keywords

lie algebras and superalgebras nilpotent groups algebra classification and gradings

Cite

@article{arxiv.2406.04036,
  title  = {A classification of nilpotent compatible Lie algebras},
  author = {Manuel Ladra and Bernardo Leite da Cunha and Samuel A. Lopes},
  journal= {arXiv preprint arXiv:2406.04036},
  year   = {2024}
}

Comments

To appear in Rendiconti del Circolo Matematico di Palermo Series 2

A classification of nilpotent compatible Lie algebras

Abstract

Keywords

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