Poisson and Symplectic structures, Hamiltonian action, momentum and reduction

Autor:	Roubtsov, Vladimir, Dutykh, Denys
Rok vydání:	2020
Předmět:	Mathematics - Differential Geometry Mathematical Physics Mathematics - Quantum Algebra Nonlinear Sciences - Exactly Solvable and Integrable Systems 53D17 37K05 (primary) 53D05 53D20 (secondary)
Druh dokumentu:	Working Paper
Popis:	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. Comment: 31 pages, 14 references, alphabetical index. Other author's papers can be downloaded at http://www.denys-dutykh.com/
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2003.14173 Zobrazit plný text záznamu View this record from Arxiv