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 NameAffiliation
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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