Degenerations of Poisson-type algebras

被引：0

作者：

Abdelwahab, Hani ^{[1
]}

Ouaridi, Amir Fernandez ^{[2
]}

Kaygorodov, Ivan ^{[3
,4
,5
]}

机构：

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

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

[3] Univ Beira Interior, CMA UBI, Covilha, Portugal

[4] Moscow Ctr Fundamental & Appl Math, Moscow, Russia

[5] St Petersburg State Univ, St Petersburg, Russia

来源：

RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO | 2025年 / 74卷 / 01期

基金：

俄罗斯科学基金会;

关键词：

<italic>Poisson-type algebras</italic>; <italic>Classification</italic>; <italic>Degeneration</italic>; NILPOTENT LIE-ALGEBRAS; GEOMETRIC CLASSIFICATION; NOVIKOV ALGEBRAS; DIMENSION LESS; DEFORMATION; VARIETIES;

D O I：

10.1007/s12215-024-01152-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The degenerations of Poisson-type algebras are studied in the following varieties in dimension two: Leibniz-Poisson algebras, transposed Leibniz-Poisson algebras, Novikov-Poisson algebras, commutative pre-Lie algebras, anti-pre-Lie Poisson algebras and pre-Poisson algebras. For these varieties, the algebraic and geometric classifications are given. Also, the complete graph of degenerations is obtained, together with the description of the orbit closures of each of its algebras and parametric families up to isomorphism.

引用

页数：43

共 60 条

[1] Degenerations of Poisson algebras [J].