可交换Hopf代数和Hopf大括号上的Rota-Baxter算子

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2025-07-01 DOI:10.1016/j.geomphys.2025.105580

Huihui Zheng , Liangyun Zhang , Tianshui Ma , Li Guo

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引用次数: 0

摘要

研究了带Hopf括号的协交换Hopf代数上的Rota-Baxter算子与Yang-Baxter方程的关系，重点研究了协交换Hopf括号在Rota-Baxter Hopf代数中的嵌入问题。通过Hopf大括号，建立了可交换Hopf代数上的相对Rota-Baxter算子与双射1-环之间的联系。最后，我们引入了对称Hopf支撑的概念，并建立了对称Hopf支撑与Rota-Baxter Hopf代数之间的关系。

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Rota-Baxter operators on cocommutative Hopf algebras and Hopf braces

This paper studies the relationship of Rota-Baxter operators on cocommutative Hopf algebras with Hopf braces and the Yang-Baxter equation, with emphasis on the embedding of cocommutative Hopf braces into Rota-Baxter Hopf algebras. Through Hopf braces, we establish a connection between relative Rota-Baxter operators on cocommutative Hopf algebras and bijective 1-cocycles. Finally, we introduce the notion of symmetric Hopf braces, and establish the relationship between symmetric Hopf braces and Rota-Baxter Hopf 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