2020/03/28 by Vladimir Roubtsov, Denys Dutykh, Roubtsov, Vladimir +1
Mathematics · Physics and Astronomy · #37K05 (primary) #53D05 #53D17 #53D20 (secondary) #Advanced Differential Geometry Research #Algebraic and Geometric Analysis #Differential Geometry (math.DG) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.2003.14173
openalex publication_date 2020/03/28 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
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.