| 白永强,付会娟,裴 明.非交换微分及可积系统的统一零曲率表示[J].数学年刊A辑,2016,37(4):421~432 |
| 非交换微分及可积系统的统一零曲率表示 |
| Noncommutative Differential Calculus and the Unified Zero CurvatureRepresentation of Integrable Systems |
| Received:September 22, 2014 Revised:January 15, 2016 |
| DOI： |
| 中文关键词: 零曲率, 非交换微分, 可积性, 联络 |
| 英文关键词:Zero curvature, Noncommutative differential
calculus, Integrability, Connection |
| 基金项目:本文受到国家自然科学基金(No.10801045)和河南省科技厅项目(No.152300410062) 的资助. |
| Author Name | Affiliation | | BAI Yongqiang | Institute of Contemporary Mathematics, Henan University, Kaifeng 475004, Henan, China
School of Mathematics and Statistics, Henan University,
Kaifeng 475004, Henan, China. | | FU Huijuan | School of Mathematics and Statistics,
Henan University, Kaifeng 475004, Henan, China. | | PEI
Ming | School of Mathematics and Statistics,
Henan University, Kaifeng 475004, Henan, China. |
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| 中文摘要: |
| 基于导数的微分在非交换几何、非交换规范理论和可积系统中都有十分重要的作用.
本文从一类基于导数的微分出发给出了联络和曲率形式. 利用这一理论,
作者给出了连续、半离散和离散可积系统的统一零曲率表示. |
| 英文摘要: |
| Derivation-based differential calculus is of
great importance in noncommutative geometry, noncommutative gauge
theory and integrable systems. This paper gives the
connection and curvature from a class of deformed derivation-based
differential calculus. By means of this theory, the authors obtain the
zero-curvature representation of the continuous, semi-discrete and discrete integrable systems in an
unified manner. |
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