Super Kupershmidt operator and the Yang-Baxter equation in Malcev superalgebras

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2025-09-29 DOI:10.1016/j.geomphys.2025.105663

Yinuo Zhao , Liangyun Chen

引用次数: 0

Abstract

In this paper, we show the relationship between skew-symmetric solutions of the Yang-Baxter equation (YBE) and super Kupershmidt operators of Malcev superalgebras. First, we show that a skew-supersymmetric solution of the Yang-Baxter equation on a Malcev superalgebra can be interpreted as an super Kupershmidt operator associated to the coadjoint representation. On this basis, when considering non-degenerate skew-symmetric solutions of the Yang-Baxter equation, this connection can be enhanced with symplectic forms. We also show that super Kupershmidt operators associated with a general representation could give skew-symmetric solutions of the Yang-Baxter equation on certain semi-direct products of Malcev superalgebras. What's more, we reveal that in the case of pre-Malcev superalgebras, We can get similar results between the Yang-Baxter equation and super Kupershmidt operators.

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Malcev超代数中的超级Kupershmidt算子和Yang-Baxter方程

本文给出了Yang-Baxter方程（YBE）的偏对称解与Malcev超代数的超Kupershmidt算子之间的关系。首先，我们证明了Malcev超代数上Yang-Baxter方程的偏超对称解可以被解释为与协表示相关的超Kupershmidt算子。在此基础上，当考虑Yang-Baxter方程的非简并偏对称解时，这种联系可以用辛形式增强。我们还证明了与一般表示相关联的超Kupershmidt算子可以给出Malcev超代数的半直积上的Yang-Baxter方程的偏对称解。此外，我们揭示了在pre-Malcev超代数的情况下，我们可以在Yang-Baxter方程和超级Kupershmidt算子之间得到类似的结果。

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