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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Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2024
Автори: Abdelwahab, Hani, Kaygorodov, Ivan, Makhlouf, Abdenacer
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут математики НАН України 2024
Онлайн доступ: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
Цитувати: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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author Abdelwahab, Hani
Kaygorodov, Ivan
Makhlouf, Abdenacer
author_facet Abdelwahab, Hani
Kaygorodov, Ivan
Makhlouf, Abdenacer
citation_txt 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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container_title Symmetry, Integrability and Geometry: Methods and Applications
description 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.
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spelling Abdelwahab, Hani
Kaygorodov, Ivan
Makhlouf, Abdenacer
2026-02-11T10:38:53Z
2024
The Algebraic and Geometric Classification of Compatible Pre-Lie Algebras. Hani Abdelwahab, Ivan Kaygorodov and Abdenacer Makhlouf. SIGMA 20 (2024), 107, 20 pages
1815-0659
2020 Mathematics Subject Classification: 17A30; 17D25; 14L30
arXiv:2406.10947
https://nasplib.isofts.kiev.ua/handle/123456789/212785
https://doi.org/10.3842/SIGMA.2024.107
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.
The authors thank Amir Fernández Ouaridi for sharing some useful software programs. The work is supported by FCT UIDB/00212/2020, UIDP/00212/2020, and 2022.14950.CBM (Programa PESSOA).
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
The Algebraic and Geometric Classification of Compatible Pre-Lie Algebras
Article
published earlier
spellingShingle The Algebraic and Geometric Classification of Compatible Pre-Lie Algebras
Abdelwahab, Hani
Kaygorodov, Ivan
Makhlouf, Abdenacer
title The Algebraic and Geometric Classification of Compatible Pre-Lie Algebras
title_full The Algebraic and Geometric Classification of Compatible Pre-Lie Algebras
title_fullStr The Algebraic and Geometric Classification of Compatible Pre-Lie Algebras
title_full_unstemmed The Algebraic and Geometric Classification of Compatible Pre-Lie Algebras
title_short The Algebraic and Geometric Classification of Compatible Pre-Lie Algebras
title_sort algebraic and geometric classification of compatible pre-lie algebras
url https://nasplib.isofts.kiev.ua/handle/123456789/212785
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