On the Jordan–Chevalley decomposition problem for operator fields in small dimensions and Tempesta–Tondo conjecture

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2025-09-24 DOI:10.1016/j.geomphys.2025.105656

Alexey V. Bolsinov , Andrey Yu. Konyaev , Vladimir S. Matveev

引用次数: 0

Abstract

We explore the Jordan–Chevalley decomposition problem for an operator field in small dimensions. In dimensions three and four, we find tensorial conditions for an operator field L, similar to a nilpotent Jordan block, to possess local coordinates in which L takes a strictly upper triangular form. We prove the Tempesta–Tondo conjecture for higher order brackets of Frölicher-Nijenhuis type.

查看原文本刊更多论文

小维算子域的Jordan-Chevalley分解问题及Tempesta-Tondo猜想

研究了小维算子域的Jordan-Chevalley分解问题。在三维和四维中，我们找到了类似于幂零约当块的算子域L具有局部坐标的张量条件，其中L为严格上三角形式。证明了Frölicher-Nijenhuis型高阶括号的Tempesta-Tondo猜想。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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