Infinitesimal deformations of Poisson bi-vectors using the Kontsevich graph calculusBuring, 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).
Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review
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.
|Title of host publication||The XXV International Conference on Integrable Systems and Quantum Symmetries (ISQS-25)|
|Publisher||IOP PUBLISHING LTD|
|Number of pages||12|
|Publication status||Published - 15-Feb-2018|
|Event||25th International Conference on Integrable Systems and Quantum Symmetries, ISQS 2017 - Prague, Czech Republic|
Duration: 6-Jun-2017 → 10-Jun-2017
|Name||Journal of Physics, Conference Series|
|Conference||25th International Conference on Integrable Systems and Quantum Symmetries, ISQS 2017|
|Period||06/06/2017 → 10/06/2017|
25th International Conference on Integrable Systems and Quantum Symmetries, ISQS 2017
06/06/2017 → 10/06/2017Prague, Czech Republic