The Algebraic and Geometric Classification of Compatible Pre-Lie Algebras
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910719394447360 |
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| author | Abdelwahab, Hani Kaygorodov, Ivan Makhlouf, Abdenacer |
| author_facet | Abdelwahab, Hani Kaygorodov, Ivan Makhlouf, Abdenacer |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_10947 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Algebraic and Geometric Classification of Compatible Pre-Lie Algebras Abdelwahab, Hani Kaygorodov, Ivan Makhlouf, Abdenacer Rings and 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, 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. |
| title | The Algebraic and Geometric Classification of Compatible Pre-Lie Algebras |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2406.10947 |