三维Lie-Poisson结构的保结构变换  

Structure-preserving transformations for three-dimensional Lie-Poisson brackets

作　　者：祝玲[1] 赵晓华[1] 

机构地区：[1]浙江师范大学数理与信息工程学院,浙江金华321004

出　　处：《浙江师范大学学报（自然科学版）》2014年第2期158-163,共6页Journal of Zhejiang Normal University:Natural Sciences

基　　金：国家自然科学基金资助项目(10872183;11172269)

摘　　要：与三维Lie代数的Bianchi 13个分类相对应,欧氏空间R3上的Lie-Poisson结构也可分为13类.研究了三维Lie-Poisson结构的保结构线性变换,对应于每一类Lie-Poisson结构,获得了可逆线性变换是保结构变换的充要条件.Based on the 13 Bianchi′s classification of all three dimensional Lie algebra,all structure matrices of three-dimensional Lie-Poisson brackets were classified into 13 different types. It was studied the linear structure-preserving transformations for three-dimensional Lie-Poisson brackets and presented the necessary and sufficient conditions under which a linear transformation was structure-preserving.

关 键 词：Bianchi 分类 Lie-Poisson 结构 线性变换 保结构变换 

分 类 号：O175.14[理学—数学]