Zobrazeno 1 - 10
of 85
pro vyhledávání: '"Kiselev, Arthemy V."'
Nambu-determinant brackets on $R^d\ni x=(x^1,...,x^d)$, $\{f,g\}_d(x)=\rho(x) \det(\partial(f,g,a_1,...,a_{d-2})/\partial(x^1,...,x^d))$, with $a_i\in C^\infty(R^d)$ and $\rho\partial_x\in\mathfrak{X}^d(R^d)$, are a class of Poisson structures with (
Externí odkaz:
http://arxiv.org/abs/2409.18875
Kontsevich constructed a map between `good' graph cocycles $\gamma$ and infinitesimal deformations of Poisson bivectors on affine manifolds, that is, Poisson cocycles in the second Lichnerowicz--Poisson cohomology. For the tetrahedral graph cocycle $
Externí odkaz:
http://arxiv.org/abs/2409.15932
Kontsevich constructed a map from suitable cocycles in the graph complex to infinitesimal deformations of Poisson bi-vector fields. Under the deformations, the bi-vector fields remain Poisson. We ask, are these deformations trivial, meaning, do they
Externí odkaz:
http://arxiv.org/abs/2409.12555
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
Autor:
Buring, Ricardo, Kiselev, Arthemy V.
Publikováno v:
SciPost Phys. Proc., Vol. 14 (2023), Paper 020, pp.1--11
In Kontsevich's graph calculus, internal vertices of directed graphs are inhabited by multi-vectors, e.g., Poisson bi-vectors; the Nambu-determinant Poisson brackets are differential-polynomial in the Casimir(s) and density $\varrho$ times Levi-Civit
Externí odkaz:
http://arxiv.org/abs/2212.08063
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
Publikováno v:
Open Communications in Nonlinear Mathematical Physics, Volume 2 (December 2, 2022) ocnmp:8844
Kontsevich's graph flows are -- universally for all finite-dimensional affine Poisson manifolds -- infinitesimal symmetries of the spaces of Poisson brackets. We show that the previously known tetrahedral flow and the recently obtained pentagon-wheel
Externí odkaz:
http://arxiv.org/abs/2112.03897
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
Autor:
Kiselev, Arthemy V.
Publikováno v:
J. Phys.: Conf. Ser. (2019) Vol. 1416, Paper 012018, 1--8
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 in
Externí odkaz:
http://arxiv.org/abs/1910.05844
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