Work

The Algebraic and Geometric Classification of Compatible Pre-Lie Algebras

Year: 2024

Type: article

Abstract: 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.

Source: Symmetry Integrability and Geometry Methods and Applications

DOI: 10.3842/sigma.2024.107

Authors: Hani Abdelwahab, Ivan Kaygorodov, Abdenacer Makhlouf

Institutions: Mansoura University, University of Beira Interior, Université de Haute-Alsace

Language: English

Topic: Advanced Topics in Algebra

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Fundação para a Ciência e a Tecnologia

Awards: Centro de Matemática e Aplicações da Universidade da Beira Interior, Centro de Matemática e Aplicações da Universidade da Beira Interior