广义泊松代数：可解性及其构造

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2025-09-18 DOI:10.1016/j.geomphys.2025.105649

Xinru Cao , Zafar Normatov , Bakhrom Omirov , Jie Ruan

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引用次数: 0

摘要

本文研究了广义泊松代数中的幂零可解结构，在此背景下建立了恩格尔定理和李定理的类似物。本文给出了几种广义泊松代数的构造，包括由零丝形和丝形结合交换代数导出的广义泊松代数的构造，并探讨了通过单位共轭和广义朗斯基李代数的扩展。利用极化技术，建立了代数结构之间的基本等价，并对可容许代数进行了刻画。最后，给出了三维范围内复幂零广义泊松代数的一个完整分类。

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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On generalized Poisson algebras: Solvability and constructions

This paper investigates nilpotent and solvable structures in generalized Poisson algebras, establishing analogues of Engel's and Lie's theorems within this context. We present several constructions of generalized Poisson algebras, including those derived from null-filiform and filiform associative commutative algebras, and explore extensions through unit adjunction and generalized Wronskian Lie algebras. Using polarization techniques, we establish fundamental equivalences between algebraic structures and characterize admissible algebras. Finally, we provide a complete classification of complex nilpotent generalized Poisson algebras up to dimension three.

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来源期刊

Journal of Geometry and Physics 物理-物理：数学物理

CiteScore

2.90

自引率

6.70%

发文量

205

审稿时长

64 days

期刊介绍： The Journal of Geometry and Physics is an International Journal in Mathematical Physics. The Journal stimulates the interaction between geometry and physics by publishing primary research, feature and review articles which are of common interest to practitioners in both fields. The Journal of Geometry and Physics now also accepts Letters, allowing for rapid dissemination of outstanding results in the field of geometry and physics. Letters should not exceed a maximum of five printed journal pages (or contain a maximum of 5000 words) and should contain novel, cutting edge results that are of broad interest to the mathematical physics community. Only Letters which are expected to make a significant addition to the literature in the field will be considered. The Journal covers the following areas of research: Methods of: • Algebraic and Differential Topology • Algebraic Geometry • Real and Complex Differential Geometry • Riemannian Manifolds • Symplectic Geometry • Global Analysis, Analysis on Manifolds • Geometric Theory of Differential Equations • Geometric Control Theory • Lie Groups and Lie Algebras • Supermanifolds and Supergroups • Discrete Geometry • Spinors and Twistors Applications to: • Strings and Superstrings • Noncommutative Topology and Geometry • Quantum Groups • Geometric Methods in Statistics and Probability • Geometry Approaches to Thermodynamics • Classical and Quantum Dynamical Systems • Classical and Quantum Integrable Systems • Classical and Quantum Mechanics • Classical and Quantum Field Theory • General Relativity • Quantum Information • Quantum Gravity