The Algebraic and Geometric Classification of Compatible Pre-Lie Algebras
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.
Keywords
Cite
@article{arxiv.2406.10947,
title = {The Algebraic and Geometric Classification of Compatible Pre-Lie Algebras},
author = {Hani Abdelwahab and Ivan Kaygorodov and Abdenacer Makhlouf},
journal= {arXiv preprint arXiv:2406.10947},
year = {2024}
}
Comments
Some text overlap with our paper arXiv:2403.17193 is caused by our use here of basically the same method for discovering the main result, but the variety considered here and the results are totally different from arXiv:2403.17193