Open problems in the Kontsevich graph construction of Poisson bracket symmetries
arXiv:1910.05844 · doi:10.1088/1742-6596/1416/1/012018
Abstract
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.
arXiv commentProc. 26th Int. conference on Integrable Systems and Quantum Symmetries -- ISQS'26 (8--12 July 2019, CVUT Prague, CZ), 8 pages
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