Noncommutative Differential Calculus and Its Application on the Lattice

Chinese Quarterly Journal of Mathematics ›› 2007, Vol. 22 ›› Issue (2): 245-251.

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)；

Abstract

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

CLC Number:

O186.15

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.

Noncommutative Differential Calculus and Its Application on the Lattice

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