TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysProc.14.020
TI  - The tower of Kontsevich deformations for Nambu-Poisson structures on $\mathbb{R}^d$: Dimension-specific micro-graph calculus
PY  - 2023/11/23
UR  - https://scipost.org/SciPostPhysProc.14.020
JF  - SciPost Physics Proceedings
JA  - SciPost Phys. Proc.
VL  - 
IS  - 14
SP  - 020
A1  - Buring, Ricardo
AU  - Kiselev, Arthemy V.
AB  - 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 $\mathbb{R}^2$.
ER  -

@Article{10.21468/SciPostPhysProc.14.020,
	title={{The tower of Kontsevich deformations for Nambu-Poisson structures on $\mathbb{R}^d$: Dimension-specific micro-graph calculus}},
	author={Ricardo Buring and Arthemy V. Kiselev},
	journal={SciPost Phys. Proc.},
	pages={020},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhysProc.14.020},
	url={https://scipost.org/10.21468/SciPostPhysProc.14.020},
}