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,...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2024 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2024
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/212785 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | The Algebraic and Geometric Classification of Compatible Pre-Lie Algebras. Hani Abdelwahab, Ivan Kaygorodov and Abdenacer Makhlouf. SIGMA 20 (2024), 107, 20 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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.
|
|---|---|
| ISSN: | 1815-0659 |