叶上泊松连接的平均方法及其应用

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2020-01-01 DOI:10.3934/jgm.2020015

M. Avendaño-Camacho, Isaac Hasse-Armengol, E. Velasco-Barreras, Y. Vorobiev

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引用次数: 1

摘要

在具有紧李群的正则和共切作用的泊松叶上，我们描述了泊松连接的平均方法。在这种情况下，我们推广了前人关于汉纳-贝里连接对泊松纤维束的哈密顿作用和局部哈密顿作用的一些结果。我们对连接的平均方法的主要应用是构造由泊松叶理的de Rham-Casimir复形的2环参数化的不变Dirac结构。

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The method of averaging for Poisson connections on foliations and its applications

On a Poisson foliation equipped with a canonical and cotangential action of a compact Lie group, we describe the averaging method for Poisson connections. In this context, we generalize some previous results on Hannay-Berry connections for Hamiltonian and locally Hamiltonian actions on Poisson fiber bundles. Our main application of the averaging method for connections is the construction of invariant Dirac structures parametrized by the 2-cocycles of the de Rham-Casimir complex of the Poisson foliation.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

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