诺维科夫代数的同构和无边扩展

IF 1.6 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2024-07-02 DOI:10.1016/j.geomphys.2024.105263

Xiaosheng Peng, Youjun Tan

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引用次数: 0

摘要

诺维科夫代数的非等边扩展模块是一个短精确序列，它引起的模块结构与规定的模块结构完全相同。通过应用切瓦利-艾伦伯格类型的同调，我们证明了所有无性扩展都是由准共轭双线性形式给出的第二同调群子空间分类的。

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Cohomologies and abelian extensions of Novikov algebras

An abelian extension of a Novikov algebra by a module is a short exact sequence which induces exactly the same module structure as prescribed. By applying the cohomology of Chevalley-Eilenberg type we show that all abelian extensions are classified by the subspace of the second cohomology group given by quasi-associative bilinear forms.

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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