Para-Kähler李2 -代数，前李2 -双代数和2阶经典Yang-Baxter方程

IF 1.6 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2025-07-02 DOI:10.1016/j.geomphys.2025.105582

Jiefeng Liu , Tongtong Yue , Qi Wang

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引用次数: 0

摘要

我们引入了para-Kähler严格李2代数的概念，它可以看作是para-Kähler李代数的一个分类。为了从严格前李2-代数的角度研究para-Kähler严格李2-代数，我们引入了严格前李2-代数的Manin三元组、匹配对和双代数理论，并建立了它们之间的等价关系。利用李2-代数的上同调理论，研究了共边严格前李2-代数，并在严格前李2-代数中引入了2阶经典Yang-Baxter方程。二阶经典Yang-Baxter方程的解对于构造严格前李2代数和para-Kähler严格李2代数是有用的。特别地，从严格pre-Lie - 2-代数中得到了严格pre-Lie - 2双代数的自然构造。

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Para-Kähler Lie 2-algebras, pre-Lie 2-bialgebras and 2-graded classical Yang-Baxter equations

We introduce a notion of a para-Kähler strict Lie 2-algebra, which can be viewed as a categorification of a para-Kähler Lie algebra. In order to study para-Kähler strict Lie 2-algebra in terms of strict pre-Lie 2-algebras, we introduce the Manin triples, matched pairs and bialgebra theory for strict pre-Lie 2-algebras and the equivalent relationships between them are also established. Using the cohomology theory of Lie 2-algebras, we study the coboundary strict pre-Lie 2-algebras and introduce 2-graded classical Yang-Baxter equations in strict pre-Lie 2-algebras. The solutions of the 2-graded classical Yang-Baxter equations are useful to construct strict pre-Lie 2-algebras and para-Kähler strict Lie 2-algebras. In particular, there is a natural construction of strict pre-Lie 2-bialgebras from the strict pre-Lie 2-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