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 Curvature Representation of Integrable Systems

作　　者：白永强[1,2] 付会娟[2] 裴明[2] BAI Yongqiang FU Huijuan PEI Ming(Institute of Contemporary Mathematics, Henan University, Kaifeng 475004, Henan, China School of Mathematics and Statistics, Henan University, Kaifeng 475004, Henan, China)

机构地区：[1]河南大学现代数学研究所,河南开封475004 [2]河南大学数学与统计学院,河南开封475004

出　　处：《数学年刊（A辑）》2016年第4期421-432,共12页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.10801045);河南省科技厅项目(No.152300410062)的资助

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.Derivation-based differential calculus is of great importance in noncommutative geometry, noncommutative gauge theory and integrable systems. This paper gives the con- nection 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.

关 键 词：零曲率 非交换微分 可积性 联络 

分 类 号：O175[理学—数学]