Differential Algebraic Framework for Noncommutative Geometry: Constructive Methods for Noncommutative PDEs and Geometric Structures

2025 · doi:10.22541/au.176159472.24682400/v1
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Abstract

本文建立了一个全面的非交换几何微分代数框架，将建设性方法从经典微分几何扩展到非交换空间。我们定义了非交换微分几何闭包 K NCGeo，这是一种通过递归附加过程构建的微分闭扩展，系统地结合了非交换几何对象、光谱数据、曲率算子和基本解。该闭包为显式表示大类非交换偏微分方程 （PDE） 的解提供了一个通用域，包括非交换拉普拉斯方程、曲率流和谱几何方程。在这个闭包中，我们证明解允许尊重底层代数和几何结构的统一谱表示。该框架严格解决了非交换性、谱约束和算子-理论关系的挑战，同时保留了梯度代数结构和几何兼容性条件。我们提供了详细的存在和表示定理的建设性证明，推导了在算子范数中具有严格误差范围的显式解公式，并在适当的非交换函数空间中建立了收敛标准。 Supplementary Material File (non_commutative_geotry.pdf) - Download - 417.15 KB Information & Authors Information Version history Copyright This work is licensed under a Creative Commons Attribution 4.0 International License

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Authors Metrics & Citations Metrics Article Usage 138views 118downloads Citations Download citation Dongqi Liu, shifa liu. Differential Algebraic Framework for Noncommutative Geometry: Constructive Methods for Noncommutative PDEs and Geometric Structures. Authorea. 27 October 2025. DOI: https://doi.org/10.22541/au.176159472.24682400/v1 DOI: https://doi.org/10.22541/au.176159472.24682400/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu.

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last seen: 2026-05-20T01:45:00.602351+00:00