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arXiv · 2406.10947

The Algebraic and Geometric Classification of Compatible Pre-Lie Algebras

Hani Abdelwahab·Ivan Kaygorodov·Abdenacer Makhlouf
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Abstract

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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Hani Abdelwahab, Ivan Kaygorodov, Abdenacer Makhlouf. 2024-06-16. The Algebraic and Geometric Classification of Compatible Pre-Lie Algebras. https://doi.org/10.3842/sigma.2024.107

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