The Algebraic and Geometric Classification of Compatible Pre-Lie Algebras

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,...

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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
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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

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Zusammenfassung: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, we obtain the classification of complex 2-dimensional compatible commutative associative, compatible associative, and compatible Novikov algebras. In addition, we consider the geometric classification of varieties of cited algebras, that is, the description of their irreducible components.
ISSN:1815-0659