Differential-difference Complex and the Poincar′e Lemma  

微分差分复形及其庞加莱引理（英文）

作　　者：白永强 阎国栋 

机构地区：[1]Institute of Contemporary Mathematics, Henan University [2]School of Mathematics and Statistics, Henan University

出　　处：《Chinese Quarterly Journal of Mathematics》2015年第1期1-11,共11页数学季刊（英文版）

基　　金：Supported by the NSFC(10801045)

摘　　要：Dierential geometry play a fundamental role in discussing partial dierential equations（PDEs） in mathematical physics. Recently discrete dierential geometry is an active mathematical terrain, which aims at the development and application of discrete equivalents of the geometric notions and methods of dierential geometry. In this paper, a discrete theory of exterior dierential calculus and the analogue of the Poincar′e lemma for dierential-dierence complex are proposed. They provide an intrinsic idea for developing the theory to discuss the integrability of dierence equations.

关 键 词：noncommutative differential calculus differential-difference complex EXACT 

分 类 号：O186.15[理学—数学]