| 三维Lie-Poisson结构的保结构变换 |
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| 引用本文： | 祝玲,赵晓华.三维Lie-Poisson结构的保结构变换[J].浙江师范大学学报(自然科学版),2014(2):158-163. |
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| 作者姓名： | 祝玲 赵晓华 |
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| 作者单位： | 浙江师范大学数理与信息工程学院,浙江金华321004 |
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| 基金项目： | 国家自然科学基金资助项目（10872183;11172269） |
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| 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.
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| 关 键 词： | Bianchi分类 Lie-Poisson结构 线性变换 保结构变换 |
Structure-preserving transformations for three-dimensional Lie-Poisson brackets |
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| ZHU Ling,ZHAO Xiaohua.Structure-preserving transformations for three-dimensional Lie-Poisson brackets[J].Journal of Zhejiang Normal University Natural Sciences,2014(2):158-163. |
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| Authors: | ZHU Ling ZHAO Xiaohua |
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| Institution: | (College of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua Zhejiang 321004, China) |
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| Abstract: | 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. |
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| Keywords: | Bianchi′s classification Lie-Poisson structure linear transformation structure-preserving transformation |
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