Kontsevich graphs act on Nambu-Poisson brackets, VI. Open problems
Abstract
Kontsevich's graphs from deformation quantisation allow encoding multi-vectors whose coefficients are differential-polynomial in components of Poisson brackets on finite-dimensional affine manifolds. The calculus of Kontsevich graphs can be made dimension-specific for the class of Nambu--Poisson brackets given by Jacobian determinants. Using the Kontsevich--Nambu micro-graphs in dimensions , we explore the open problem of (non)triviality for Kontsevich's tetrahedral graph cocycle action on the space of Nambu--Poisson brackets. We detect a conjecturally infinite new set of differential-polynomial identities for Jacobian determinants of arbitrary sizes .
Cite
@article{arxiv.2511.06121,
title = {Kontsevich graphs act on Nambu-Poisson brackets, VI. Open problems},
author = {Mollie S. Jagoe Brown and Arthemy V. Kiselev},
journal= {arXiv preprint arXiv:2511.06121},
year = {2025}
}
Comments
Based on the talk given by the first author at the XIII International symposium on Quantum Theory and Symmetries -- QTS13 (Yerevan, Armenia, 28 July -- 1 August 2025); 1 table, 8 pages