Poisson仿射群的性质  

Properties of Poisson Affine Group

作　　者：侯传燕[1] 杨祺[1] 何勇[1] 

机构地区：[1]新疆师范大学数学科学学院,新疆乌鲁木齐830054

出　　处：《新疆师范大学学报（自然科学版）》2011年第4期65-67,共3页Journal of Xinjiang Normal University(Natural Sciences Edition)

基　　金：新疆师范大学优秀青年教师科研启动基金资助(XJNU1010)

摘　　要：Poisson流形在现代Hamilton系统中扮演了很重要的角色,基于以前的研究,文章在李群上赋予poisson结构,提出了poisson仿射群的概念,在此基础上定义了Poisson括号,并证明了此poisson括号满足双线性,反称性,Leibniz法则及Jacobi恒等式,同时讨论了Poisson映射和Poisson作用的性质。Poisson manifold, which act as the phase space of the generalized Hamilton system, Based on the work by the period. In this paper, Lie Group is endued with Poisson structure, Definition of Pois- son affine group and Poisson bracket are given, and the conclusion are proved that Poisson bracket satisfies bilinear try , antisymmetry, Leibniz principle and Jacobi identity. At the same time, some proposition a- bout Poisson map and Poisson functions are discussed.

关 键 词：李群 仿射群 poisson仿射群 POISSON结构 POISSON括号 

分 类 号：O157.7[理学—数学]