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arXiv · 2209.09150

Degenerations of Poisson algebras

Hani Abdelwahab·Amir Fernández Ouaridi·Cándido Martín González
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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 $3$-dimensional Poisson algebras. In addition, we study the geometric classification, the graph of degenerations and the closures of the orbits of the variety of $3$-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.

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Hani Abdelwahab, Amir Fernández Ouaridi, Cándido Martín González. 2022-09-19. Degenerations of Poisson algebras. https://arxiv.org/abs/2209.09150

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