格点上的非交换微分运算及其应用

数学季刊 ›› 2007, Vol. 22 ›› Issue (2): 245-251.

格点上的非交换微分运算及其应用

1. Center of Mathematical Sciences, Zhejiang University 2. College of Mathematics and Information Science, Henan University3. Institute of Mathematics, Henan University

收稿日期:2006-02-12 出版日期:2007-06-30 发布日期:2023-11-03
作者简介:LIU Zhen(1976-),male,native of Shangqiu,Henan,a lecturer of Zhejiang University of Tech- nology,Ph.D.,engages in structure-preserving numerical algorithm.
基金资助:
Supported by the China Pcetdoctoral Science Foundation by a grant from Henan University(05YBZR014)； Supported by the Tianyuan Foundation for Mathematics of National Natural Science Foundation of China(10626016)；

Noncommutative Differential Calculus and Its Application on the Lattice

1. Center of Mathematical Sciences, Zhejiang University 2. College of Mathematics and Information Science, Henan University3. Institute of Mathematics, Henan University

Received:2006-02-12 Online:2007-06-30 Published:2023-11-03
About author:LIU Zhen(1976-),male,native of Shangqiu,Henan,a lecturer of Zhejiang University of Tech- nology,Ph.D.,engages in structure-preserving numerical algorithm.
Supported by:
Supported by the China Pcetdoctoral Science Foundation by a grant from Henan University(05YBZR014)； Supported by the Tianyuan Foundation for Mathematics of National Natural Science Foundation of China(10626016)；

摘要/Abstract

摘要： By introducing the noncommutative differential calculus on the function space of the infinite/finite set and construct a homotopy operator, one prove the analogue of the Poincare lemma for the difference complex. As an application of the differential calculus, a two dimensional integral model can be derived from the noncommutative differential calculus.

关键词: noncommutative , geometry;noncommutative , differential , calculus;Poincaré lemma;Toda lattice equation

Abstract: By introducing the noncommutative differential calculus on the function space of the infinite/finite set and construct a homotopy operator, one prove the analogue of the Poincare lemma for the difference complex. As an application of the differential calculus, a two dimensional integral model can be derived from the noncommutative differential calculus.

Key words: noncommutative , geometry;noncommutative , differential , calculus;Poincaré lemma;Toda lattice equation

中图分类号:

O186.15

刘震, 白永强, 李起升. 格点上的非交换微分运算及其应用[J]. 数学季刊, 2007, 22(2): 245-251.

LIU Zhen, BAI Yong-qiang, LI Qi-sheng. Noncommutative Differential Calculus and Its Application on the Lattice [J]. Chinese Quarterly Journal of Mathematics, 2007, 22(2): 245-251.

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