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 |
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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| _version_ | 1862690033301979136 |
|---|---|
| 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 |
| collection | DSpace DC |
| 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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| first_indexed | 2026-03-17T20:39:08Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212785 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-17T20:39:08Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| 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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