Degenerations of Poisson algebras

被引：3

作者：

Abdelwahab, Hani ^{[1
]}

Ouaridi, Amir Fernandez ^{[2
,3
]}

Gonzalez, Candido Martin ^{[4
]}

机构：

[1] Mansoura Univ, Fac Sci, Dept Math, Mansoura, Egypt

[2] Univ Cadiz, Dept Math, Puerto Real, Spain

[3] Univ Coimbra, CMUC, Dept Math, Coimbra, Portugal

[4] Univ Malaga, Dept Algebra Geometria & Topol, Fac Ciencias, Campus Teatinos S-N, Malaga 29071, Spain

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2025年 / 24卷 / 03期

关键词：

Poisson algebras; algebraic classification; geometric classification; degeneration; NILPOTENT LIE-ALGEBRAS; JORDAN ALGEBRAS; CLASSIFICATION;

D O I：

10.1142/S0219498825500872

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页数：25

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