| 非交换微分及可积系统的统一零曲率表示 |
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| 引用本文： | 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(中文版),2016,37(4):421-432. |
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| 作者姓名： | 白永强 付会娟 裴 明 |
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| 作者单位： | 河南大学现代数学研究所, 河南\开封 475004; 河南大学数学与统计学院, 河南\开封 475004.,河南大学数学与统计学院, 河南\开封 475004.,河南大学数学与统计学院, 河南\开封 475004. |
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| 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. |
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| 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.
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| 关 键 词： | 零曲率 非交换微分 可积性 联络 |
| 收稿时间： | 2014/9/22 0:00:00 |
| 修稿时间： | 2016/1/15 0:00:00 |
Noncommutative Differential Calculus and the Unified Zero Curvature
Representation of Integrable Systems |
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| BAI Yongqiang,FU Huijuan and PEI
Ming.Noncommutative Differential Calculus and the Unified Zero Curvature
Representation of Integrable Systems[J].Chinese Annals of Mathematics,2016,37(4):421-432. |
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| Authors: | BAI Yongqiang FU Huijuan and PEI
Ming |
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| Institution: | Institute of Contemporary Mathematics, Henan University, Kaifeng 475004, Henan, China;
School of Mathematics and Statistics, Henan University,
Kaifeng 475004, Henan, China.,School of Mathematics and Statistics,
Henan University, Kaifeng 475004, Henan, China. and School of Mathematics and Statistics,
Henan University, Kaifeng 475004, Henan, China. |
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| Abstract: | 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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| Keywords: | Zero curvature Noncommutative differential
calculus Integrability Connection |
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