Open problems in the Kontsevich graph construction of Poisson bracket symmetries

Autor:	Kiselev, Arthemy V.
Rok vydání:	2019
Předmět:	Mathematical Physics Mathematics - Combinatorics Mathematics - Quantum Algebra Mathematics - Symplectic Geometry Nonlinear Sciences - Exactly Solvable and Integrable Systems
Zdroj:	J. Phys.: Conf. Ser. (2019) Vol. 1416, Paper 012018, 1--8
Druh dokumentu:	Working Paper
DOI:	10.1088/1742-6596/1416/1/012018
Popis:	Poisson brackets admit infinitesimal symmetries which are encoded using oriented graphs; this construction is due to Kontsevich (1996). We formulate several open problems about combinatorial and topological properties of the graphs involved, about integrability and analytic properties of such symmetry flows (in particular, for known classes of Poisson brackets), and about cohomological, differential geometric, and quantum aspects of the theory. Keywords: Poisson bracket, Jacobi identity, infinitesimal symmetry, affine manifold, Poisson cohomology, graph complex. Comment: Proc. 26th Int. conference on Integrable Systems and Quantum Symmetries -- ISQS'26 (8--12 July 2019, CVUT Prague, CZ), 8 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1910.05844 Zobrazit plný text záznamu View this record from Arxiv