@inproceedings{6c1fb6722f4444c4b49991af29c4ade1,
title = "Infinitesimal deformations of Poisson bi-vectors using the Kontsevich graph calculus",
abstract = "Let P be a Poisson structure on a finite-dimensional affine real manifold. Can P be deformed in such a way that it stays Poisson ? The language of Kontsevich graphs provides a universal approach -with respect to all affine Poisson manifolds to finding a class of solutions to this deformation problem. For that reasoning, several types of graphs are needed. In this paper we outline the algorithms to generate those graphs. The graphs that encode deformations are classified by the number of internal vertices k; for k ≤ 4 we present all solutions of the deformation problem. For k ≥ 5, first reproducing the pentagon-wheel picture suggested at k = 6 by Kontsevich and Willwacher, we construct the heptagon-wheel cocycle that yields a new unique solution without 2-loops and tadpoles at k = 8.",
author = "Ricardo Buring and Kiselev, {Arthemy V.} and Nina Rutten",
year = "2018",
month = feb,
day = "15",
doi = "10.1088/1742-6596/965/1/012010",
language = "English",
series = "Journal of Physics, Conference Series",
publisher = "IOP PUBLISHING LTD",
number = "1",
booktitle = "The XXV International Conference on Integrable Systems and Quantum Symmetries (ISQS-25)",
note = "25th International Conference on Integrable Systems and Quantum Symmetries, ISQS 2017 ; Conference date: 06-06-2017 Through 10-06-2017",
}