Alia双代数与Lie双代数的亲和关系

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2025-08-20 DOI:10.1016/j.geomphys.2025.105627

Yanhong Guo, Bo Hou

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引用次数: 0

摘要

本文的目的是研究Alia代数的亲和关系。证明了一个Alia代数与一个无限维交换结合代数的张量积是一个无限维Alia代数。这被称为Alia代数的亲和化。我们得到了Alia余代数的一个亲和性质，并提出了Alia余代数与Alia双代数的亲和关系。特别地，我们还给出了李双代数的仿射。

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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Affinization of Alia bialgebras and Lie bialgebras

The purpose of this paper is to study the affinization of Alia algebras. We show that the tensor product of an Alia algebra and an infinite-dimensional commutative associative algebra is an infinite-dimensional Alia algebra. This is called an affinization of Alia algebras. We obtain an affinization characterization of Alia coalgebras and lift the affinization of Alia coalgebras to the Alia bialgebras. In particular, we also give the affinization of Lie bialgebras.

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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