λ-差分前李代数的同调、非阿贝尔扩展和韦尔斯精确序列

IF 1.6 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2024-07-18 DOI:10.1016/j.geomphys.2024.105280

Qinxiu Sun, QianWen Zhu

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引用次数: 0

摘要

本文的目的是研究λ-差分前李代数的同调与非阿贝尔扩展。首先，我们考虑 λ 微分前李代数的表示和同调。接下来，我们研究非标注扩展，并根据非标注同调群对非标注扩展进行分类。此外，我们还讨论了非阿贝尔扩展上的一对自动态的可诱导性，并在λ差分前李代数的背景下发展了威尔斯精确序列。最后，我们讨论了 λ 差分前李代数的无阿贝尔扩展的这些结果。

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Cohomologies, non-abelian extensions and Wells exact sequences of λ-differential pre-Lie algebras

The purpose of the present paper is to study cohomologies and non-abelian extensions of λ-differential pre-Lie algebras. First, we consider representations and cohomologies of λ-differential pre-Lie algebras. Next, we investigate non-abelian extensions and classify the non-abelian extensions in terms of non-abelian cohomology groups. Furthermore, we address the inducibility of a pair of automorphisms on non-abelian extensions and develop the Wells exact sequences in the context of λ-differential pre-Lie algebras. Finally, we discuss these results in the case of abelian extensions of λ-differential pre-Lie algebras.

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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