Local realizations of vertex algebras

IF 1.6 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2025-02-05 DOI:10.1016/j.geomphys.2025.105440

Peng Wang, Liangyun Chen

引用次数: 0

Abstract

In this paper, we mainly construct local realizations of vertex algebras for building bridges between vertex algebras and geometries. First, construct an associative algebra which we call Psi algebra that can equip the structure of any vertex algebra, and give a useful action of Psi algebra that can inherit the information of Borcherds' identities. Next, by using the path algebra and the representations of a quiver which is taken according to Psi algebra, we show a type of local realizations for any vertex algebra. Then, we give an approach to realizations of finite-dimensional vector spaces by quiver Grassmannians. Further, we can also use quiver Grassmannians to show another type of local realizations for any vertex algebra by this approach.

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顶点代数的局部实现

本文主要构造顶点代数的局部实现，用于在顶点代数和几何之间架起桥梁。首先，构造了一个可以赋予任意顶点代数结构的关联代数，我们称之为Psi代数，并给出了Psi代数继承Borcherds恒等式信息的一个有用的作用。其次，通过使用路径代数和根据Psi代数取的颤振的表示，我们展示了任意顶点代数的一种局部实现。然后，我们给出了一种用抖动格拉斯曼算子实现有限维向量空间的方法。此外，我们还可以使用颤颤格拉斯曼来展示通过这种方法对任何顶点代数的另一种类型的局部实现。

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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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