SciPost Phys. Proc. 14, 020 (2023) ·
published 23 November 2023

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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 symbolĂ—$\varrho$. 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 $\mathbb{R}^2$.
Dr Buring: "The authors are grateful to th..."
in Submissions  report on The tower of Kontsevich deformations for NambuPoisson structures on $\mathbb{R}^{d}$: dimensionspecific micrograph calculus