| 利用Dirac理论进行Poisson流形及Jacobi流形的约化(英文) |
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| 引用本文： | 刘玲,贺龙光.利用Dirac理论进行Poisson流形及Jacobi流形的约化(英文)[J].数学进展,2011(1). |
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| 作者姓名： | 刘玲 贺龙光 |
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| 作者单位： | 北京信息科技大学数学系;首都师范大学数学系; |
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| 基金项目： | Supported by Scientific Creative Platform Foundation of Beijing Municipal Commission of Education(No.PXM2008_014224_067420); Foundation of Beijing Information Science and Technology University |
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| 摘 要： | 通过将可约的Dirac以及Jacobi-Dirac结构分别分为两种类型,给出对应于Poisson流形和Jacobi流形的约化定理.这些约化定理的证明只需要进行一些直接的计算,而不需要借助于矩映射或者相容函数等复杂概念的引入.另外,给出了一些相应的例子和应用.
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| 关 键 词： | Poisson流形 Jacobi流形 Dirac结构 特征对 约化 |
Reduction of Poisson Manifolds and Jacobi Manifolds via Dirac Theory |
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| LIU Ling,HE Longguang.Reduction of Poisson Manifolds and Jacobi Manifolds via Dirac Theory[J].Advances in Mathematics,2011(1). |
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| Authors: | LIU Ling HE Longguang |
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| Institution: | LIU Ling~(1,*),HE Longguang~2 (1.Beijing Information Science and Technology University,Beijing,100192,P.R.China,2.Department of Mathematics,Capital Normal University,100037,P.R.China) |
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| Abstract: | We give two kinds of reduction relating Poisson manifolds and Jacobi manifolds by classifying reducible Dirac and Jacobi-Dirac structures into two classes,respectively.The proof needs only some direct calculation,without using the existence of momentum mappings or the introducing of admissible functions,etc..Meanwhile we present some examples and applications. |
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| Keywords: | Poisson manifolds Jacobi manifolds Dirac structures characteristic pairs reduction |
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