Noncommutative Differential Calculus and Its Application on Discrete Spaces  

作　　者：LIU Zhen BAI Yong-Qiang WU Ke GUO Han-Ying 

机构地区：[1]Center of Mathematical Sciences , Zhejiang University, Hangzhou 310027, China [2]Department of Mathematics, Zhejiang University of Technology, Hangzhou 310023,China [3]Institute of Mathematics, Henan University, Kaifeng 475001, China [4]Department of Mathematics, Capital Normal University, Beijing 100037, China [5]Institute of Theoretical Physics, the Chinese Academy of Sciences, Beijing 100080,China

出　　处：《Communications in Theoretical Physics》2008年第1期37-44,共8页理论物理通讯（英文版）

基　　金：The project supported by National Natural Science Foundation of China under Grant No.10626016;China Postdoctor Science Foundation of Henan University under Grant No.05YBZR014

摘　　要：We present the noncommutative differential calculus on the function space of the infinite set and construct a homotopy operator to prove the analogue of the Poincare lemma for the difference complex. Then the horizontal and vertical complexes are introduced with the total differential map and vertical exterior derivative. As the application of the differential calculus, we derive the schemes with the conservation of symplecticity and energy for Hamiltonian system and a two-dimensional integral models with infinite sequence of conserved currents. Then an Euler-Lagrange cohomology with symplectic structure-preserving is given in the discrete classical mechanics.

关 键 词：noncommutative differential calculus Poincare lemma horizontal and vertical complexes Euler-Lagrange cohomology 

分 类 号：O14[理学—数学]