Degenerations of Poisson algebras
Rings and Algebras
2022-09-20 v1
Abstract
We construct a method to obtain the algebraic classification of Poisson algebras defined on a commutative associative algebra, and we apply it to obtain the classification of the -dimensional Poisson algebras. In addition, we study the geometric classification, the graph of degenerations and the closures of the orbits of the variety of -dimensional Poisson algebras. Finally, we also study the algebraic classification of the Poisson algebras defined on a commutative associative null-filiform or filiform algebra and, to enrich this classification, we study the degenerations between these particular Poisson algebras.
Keywords
Cite
@article{arxiv.2209.09150,
title = {Degenerations of Poisson algebras},
author = {Hani Abdelwahab and Amir Fernández Ouaridi and Cándido Martín González},
journal= {arXiv preprint arXiv:2209.09150},
year = {2022}
}
Comments
arXiv admin note: text overlap with arXiv:2209.06403