论文标题
泊松和符号结构，哈密顿动作，动量和减少
Poisson and Symplectic structures, Hamiltonian action, momentum and reduction
论文作者
论文摘要
该手稿本质上是一本讲义的集合，由第一作者在2019年的暑期学校（波兰）撰写，并由第二作者写下来。如标题所示，此处涵盖的材料包括泊松和符号结构（Poisson歧管，泊松双载体和泊松支架），团体动作和轨道（无限动作，稳定器和邻接表示），Moment Maps Maps，Poisson和Poisson和Hamiltonian动作。最后，还讨论了相位空间的减少。最后一节介绍了泊松结构以及一些相关的概念。本文以标准参考文献以获取更多详细信息，对众所周知的材料进行了简要审查。博览会简洁，但教学。作者认为，它将作为对这个特定主题感兴趣的学生的入门展览有用。
This manuscript is essentially a collection of lecture notes which were given by the first author at the Summer School Wisl-2019, Poland and written down by the second author. As the title suggests, the material covered here includes the Poisson and symplectic structures (Poisson manifolds, Poisson bi-vectors and Poisson brackets), group actions and orbits (infinitesimal action, stabilizers and adjoint representations), moment maps, Poisson and Hamiltonian actions. Finally, the phase space reduction is also discussed. The very last section introduces the Poisson-Lie structures along with some related notions. This text represents a brief review of a well-known material citing standard references for more details. The exposition is concise, but pedagogical. The Authors believe that it will be useful as an introductory exposition for students interested in this specific topic.
