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The Algebraic and Geometric Classification of Compatible Pre-Lie Algebras

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arxiv 2406.10947 v2 pith:2IM3R6HL submitted 2024-06-16 math.RA

Hani Abdelwahab , Ivan Kaygorodov , Abdenacer Makhlouf This is my paper · ORCID
classification math.RA
keywords algebrasclassificationcompatiblepre-liealgebraicobtainassociativecomplex
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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.

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  1. Compatible anti-pre-Lie algebras

    math.RA 2024-12 reject novelty 4.0 of 10

    Compatible anti-pre-Lie algebras are introduced, characterized via negative left multiplication representations, and classified in dimension 2 by a list of 45 families.

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