Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Poisson and Symplectic structures, Hamiltonian action, momentum and reduction

Abstract : This manuscript is essentially a collection of lecture notes which were given by the first author at the Summer School Wisla-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.
Complete list of metadata

Cited literature [15 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02522156
Contributor : Denys Dutykh <>
Submitted on : Friday, March 27, 2020 - 5:46:07 PM
Last modification on : Thursday, December 3, 2020 - 3:21:02 AM

Licence


Distributed under a Creative Commons Attribution - NonCommercial - ShareAlike 4.0 International License

Identifiers

  • HAL Id : hal-02522156, version 1

Collections

Citation

Vladimir Roubtsov, Denys Dutykh. Poisson and Symplectic structures, Hamiltonian action, momentum and reduction. 2020. ⟨hal-02522156⟩

Share

Metrics

Record views

66

Files downloads

109