The Algebraic and Geometric Classification of Compatible Pre-Lie Algebras

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2024
• Hauptverfasser: Abdelwahab, Hani, Kaygorodov, Ivan, Makhlouf, Abdenacer
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2024
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/212785
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: The Algebraic and Geometric Classification of Compatible Pre-Lie Algebras. Hani Abdelwahab, Ivan Kaygorodov and Abdenacer Makhlouf. SIGMA 20 (2024), 107, 20 pages

In this paper, we develop a method to obtain the algebraic classification of compatible pre-Lie algebras from the classification of pre-Lie algebras of the same dimension. We use this method to obtain the algebraic classification of complex 2-dimensional compatible pre-Lie algebras. As a byproduct,...