Degenerations of Poisson-type algebras
Rings and Algebras
2024-03-27 v1
Abstract
The degenerations of Poisson-type algebras are studied in the following varieties in dimension two: Leibniz--Poisson algebras, transposed Leibniz--Poisson algebras, Novikov--Poisson algebras, commutative pre-Lie algebras, anti-pre-Lie Poisson algebras and pre-Poisson algebras. For these varieties, the algebraic and geometric classifications are given. Also, the complete graph of degenerations is obtained, together with the description of the orbit closures of each of its algebras and parametric families up to isomorphism.
Cite
@article{arxiv.2403.17193,
title = {Degenerations of Poisson-type algebras},
author = {Hani Abdelwahab and Amir Fernández Ouaridi and Ivan Kaygorodov},
journal= {arXiv preprint arXiv:2403.17193},
year = {2024}
}