Representations and cohomology of Rota-Baxter Lie conformal algebras

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2025-05-28 DOI:10.1016/j.geomphys.2025.105542

Jun Zhao , Bing Sun , Liangyun Chen

引用次数: 0

Abstract

In this paper, we study representations and cohomology of a weighted Rota-Baxter Lie conformal algebra. Given a weighted Rota-Baxter Lie conformal algebra

(R, T)

and its representation

(M, F)

, we define its cohomology and discuss the relation with the cohomology of weighted Rota-Baxter associative conformal algebra. As applications of the cohomology theory, we study abelian extensions, formal deformations of a weighted Rota-Baxter Lie conformal algebra.

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Rota-Baxter Lie共形代数的表示与上同调

本文研究了一类加权Rota-Baxter Lie共形代数的表示和上同调。给出一个加权Rota-Baxter Lie共形代数（R，T）及其表示（M，F），定义了它的上同调，并讨论了它与加权Rota-Baxter结合共形代数上同调的关系。作为上同调理论的应用，我们研究了加权Rota-Baxter Lie共形代数的abelian扩展和形式变形。

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