n-Lie-Rinehart代数的（共）态射及其在Nambu-Poisson流形中的应用

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2025-05-16 DOI:10.1016/j.geomphys.2025.105536

Yanhui Bi , Zhixiong Chen , Tao Zhang

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引用次数: 0

摘要

本文给出了n-Lie-Rinehart代数的态射和共胚的统一描述。我们证明了这些态射和共胚可以看作n-Lie-Rinehart代数的ψ和的两个子代数。我们也给出了n-Lie代数群的态射和共胚的类似描述。证明了具有Nambu-Poisson结构的向量束的范畴与其具有n-Lie代数结构的对偶束的范畴是等价的。

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On (co-)morphisms of n-Lie-Rinehart algebras with applications to Nambu-Poisson manifolds

In this paper, we give a unified description of morphisms and comorphisms of n-Lie-Rinehart algebras. We show that these morphisms and comorphisms can be regarded as two subalgebras of the ψ-sum of n-Lie-Rinehart algebras. We also provide similar descriptions for morphisms and comorphisms of n-Lie algebroids. It is proved that the category of vector bundles with Nambu-Poisson structures and the category of their dual bundles with n-Lie algebroid structures are equivalent to each other.

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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