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The Algebraic and Geometric Classification of Compatible Pre-Lie Algebras
Symmetry, integrability and geometry: methods and applications, Tome 20 (2024) Cet article a éte moissonné depuis la source Math-Net.Ru

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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 its irreducible components.
Keywords: geometric classification.
Mots-clés : compatible algebra, compatible associative algebra, compatible pre-Lie algebra, algebraic classification 
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}
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Hani Abdelwahab; Ivan Kaygorodov; Abdenacer Makhlouf. The Algebraic and Geometric Classification of Compatible Pre-Lie Algebras. Symmetry, integrability and geometry: methods and applications, Tome 20 (2024). http://geodesic.mathdoc.fr/item/SIGMA_2024_20_a106/

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