The tower of Kontsevich deformations for Nambu-Poisson structures on $\mathbb{R}^d$: Dimension-specific micro-graph calculus
Ricardo Buring, Arthemy V. Kiselev
SciPost Phys. Proc. 14, 020 (2023) · published 23 November 2023
- doi: 10.21468/SciPostPhysProc.14.020
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Proceedings event
34th International Colloquium on Group Theoretical Methods in Physics
Abstract
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 - Civita symbol. We resolve the old vertices into subgraphs such that every new internal vertex contains one Casimir or one Levi - Civita symbol×$\varrho$. Using this micro - graph calculus, we show that Kontsevich's tetrahedral $\gamma_3$-flow on the space of Nambu - determinant Poisson brackets over $\mathbb{R}^3$ is a Poisson coboundary: we realize the trivializing vector field $\vec{X}$ over $\mathbb{R}^3$ using micro - graphs. This $\vec{X}$ projects to the known trivializing vector field for the $\gamma_3$-flow over $\mathbb{R}^2$.
Authors / Affiliations: mappings to Contributors and Organizations
See all Organizations.- 1 Ricardo Buring,
- 2 Arthemy V. Kiselev
- 1 Johannes Gutenberg-Universität Mainz / Johannes Gutenberg University of Mainz
- 2 Rijksuniversiteit Groningen / University of Groningen [UG]
- Deutsche Forschungsgemeinschaft / German Research FoundationDeutsche Forschungsgemeinschaft [DFG]
- Institut des Hautes Études Scientifiques, Université Paris-Saclay
- Johannes Gutenberg-Universität Mainz / Johannes Gutenberg University of Mainz
- Nokia Foundation
- Rijksuniversiteit Groningen / University of Groningen [UG]