English

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 33-dimensional Poisson algebras. In addition, we study the geometric classification, the graph of degenerations and the closures of the orbits of the variety of 33-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