Associativity certificates for Kontsevich's star-product $\star$ mod $\bar{o}(\hbar^k)$: $k\leqslant 6$ unlike $k\geqslant7$

Autor: Buring, Ricardo, Kiselev, Arthemy V.

Publikováno v: Journal of Physics: Conference Series, Vol.2667 (2023), Paper 012080, pp.1--8

The formula $\star$ mod $\bar{o}(\hbar^k)$ of Kontsevich's star-product with harmonic propagators was known in full at $\hbar^{k\leqslant 6}$ since 2018 for generic Poisson brackets, and since 2022 also at $k=7$ for affine brackets. We discover that

Externí odkaz: http://arxiv.org/abs/2309.16664

Kontsevich's star-product up to order 7 for affine Poisson brackets: where are the Riemann zeta values?

Autor: Buring, Ricardo, Kiselev, Arthemy V.

Publikováno v: Open Communications in Nonlinear Mathematical Physics, Proceedings: OCNMP Conference, Bad Ems (Germany), 23-29 June 2024 (October 3, 2024) ocnmp:14168

The Kontsevich star-product admits a well-defined restriction to the class of affine -- in particular, linear -- Poisson brackets; its graph expansion consists only of Kontsevich's graphs with in-degree $\leqslant 1$ for aerial vertices. We obtain th

Externí odkaz: http://arxiv.org/abs/2209.14438

Universal cocycles and the graph complex action on homogeneous Poisson brackets by diffeomorphisms

Autor: Buring, Ricardo, Kiselev, Arthemy V.

Publikováno v: Physics of Particles and Nuclei Letters (2020) Vol.17, no.5, 707--713

The graph complex acts on the spaces of Poisson bi-vectors $P$ by infinitesimal symmetries. We prove that whenever a Poisson structure is homogeneous, i.e. $P = L_{\vec{V}}(P)$ w.r.t. the Lie derivative along some vector field $\vec{V}$, but not quad

Externí odkaz: http://arxiv.org/abs/1912.12664

The Kontsevich graph orientation morphism revisited

Autor: Kiselev, Arthemy V., Buring, Ricardo

Publikováno v: Banach Center Publications (2021) Vol. 123 "Homotopy algebras, deformation theory and quantization", 123--139

The orientation morphism $Or(\cdot)(P)\colon \gamma\mapsto\dot{P}$ associates differential-polynomial flows $\dot{P}=Q(P)$ on spaces of bi-vectors $P$ on finite-dimensional affine manifolds $N^d$ with (sums of) finite unoriented graphs $\gamma$ with

Externí odkaz: http://arxiv.org/abs/1904.13293

Poisson brackets symmetry from the pentagon-wheel cocycle in the graph complex

Autor: Buring, Ricardo, Kiselev, Arthemy V., Rutten, Nina J.

Publikováno v: Physics of Particles and Nuclei (2018) Vol. 49, No. 5, 924--928

Kontsevich designed a scheme to generate infinitesimal symmetries $\dot{\mathcal{P}} = \mathcal{Q}(\mathcal{P})$ of Poisson brackets $\mathcal{P}$ on all affine manifolds $M^r$; every such deformation is encoded by oriented graphs on $n+2$ vertices a

Externí odkaz: http://arxiv.org/abs/1712.05259