Degenerations of Poisson Algebras

IF 0.5 3区数学 Q3 MATHEMATICS

Journal of Algebra and Its Applications Pub Date : 2023-11-01 DOI:10.1142/s0219498825500872

Hani Abdelwahab, Amir Fernandez Ouaridi, Candido Martin Gonzalez

引用次数: 1

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 [Formula: see text]-dimensional Poisson algebras. In addition, we study the geometric classification, the graph of degenerations and the closures of the orbits of the variety of [Formula: see text]-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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泊松代数的退化

我们构造了一种方法来获得定义在交换关联代数上的泊松代数的代数分类，并将其应用于[公式:见文]-维泊松代数的分类。此外，我们研究了各种[公式:见文]维泊松代数的几何分类、退化图和轨道闭包。最后，我们还研究了在交换结合的零丝形或丝形代数上定义的泊松代数的代数分类，并研究了这些特定泊松代数之间的退化，以丰富这一分类。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Algebra and Its Applications 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

226

审稿时长

4-8 weeks

期刊介绍： The Journal of Algebra and Its Applications will publish papers both on theoretical and on applied aspects of Algebra. There is special interest in papers that point out innovative links between areas of Algebra and fields of application. As the field of Algebra continues to experience tremendous growth and diversification, we intend to provide the mathematical community with a central source for information on both the theoretical and the applied aspects of the discipline. While the journal will be primarily devoted to the publication of original research, extraordinary expository articles that encourage communication between algebraists and experts on areas of application as well as those presenting the state of the art on a given algebraic sub-discipline will be considered.