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ЖУРНАЛЫ // Symmetry, Integrability and Geometry: Methods and Applications // Архив

SIGMA, 2024, том 20, 107, 20 стр. (Mi sigma2109)

The Algebraic and Geometric Classification of Compatible Pre-Lie Algebras

Hani Abdelwahaba, Ivan Kaygorodovb, Abdenacer Makhloufc

a Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt
b CMA-UBI, University of Beira Interior, Covilhã, Portugal
c IRIMAS- Département de Mathématiques, University of Haute Alsace, Mulhouse, France

Аннотация: 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.

Ключевые слова: compatible algebra, compatible associative algebra, compatible pre-Lie algebra, algebraic classification, geometric classification.

MSC: 17A30, 17D25, 14L30

Поступила: 22 августа 2024 г.; в окончательном варианте 18 ноября 2024 г.; опубликована 28 ноября 2024 г.

Язык публикации: английский

DOI: 10.3842/SIGMA.2024.107


ArXiv: 2406.10947


© МИАН, 2025