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,...
Збережено в:
| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2024 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2024
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| 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 |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | 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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| ISSN: | 1815-0659 |