Publication

Infinitesimal deformations of Poisson bi-vectors using the Kontsevich graph calculus

Buring, R., Kiselev, A. V. & Rutten, N., 15-Feb-2018, The XXV International Conference on Integrable Systems and Quantum Symmetries (ISQS-25). IOP PUBLISHING LTD, 12 p. 012010. (Journal of Physics, Conference Series; vol. 965, no. 1).

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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.

Original languageEnglish
Title of host publicationThe XXV International Conference on Integrable Systems and Quantum Symmetries (ISQS-25)
PublisherIOP PUBLISHING LTD
Number of pages12
Publication statusPublished - 15-Feb-2018
Event25th International Conference on Integrable Systems and Quantum Symmetries, ISQS 2017 - Prague, Czech Republic
Duration: 6-Jun-201710-Jun-2017

Publication series

NameJournal of Physics, Conference Series
PublisherIoP Publishing
Number1
Volume965
ISSN (Print)1742-6588

Conference

Conference25th International Conference on Integrable Systems and Quantum Symmetries, ISQS 2017
CountryCzech Republic
CityPrague
Period06/06/201710/06/2017

Event

25th International Conference on Integrable Systems and Quantum Symmetries, ISQS 2017

06/06/201710/06/2017

Prague, Czech Republic

Event: Conference

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