$\u211d^{d}$上Nambu-Poisson结构的Kontsevich形变塔：维度特定的微图演算
The tower of Kontsevich deformations for Nambu-Poisson structures on $\mathbb{R}^{d}$: dimension-specific micro-graph calculus
AI总结：
本文提出维度特定的微图演算，将旧顶点分解为含Casimir或Levi-Civita符号乘密度的子图，证明ℝ³上Nambu-行列式Poisson括号的Kontsevich四面体γ₃-流是Poisson上边缘，并构造其平凡化向量场。
摘要：
在Kontsevich的图演算中，有向图的内顶点由多向量占据，例如Poisson双向量；Nambu-行列式Poisson括号是Casimir函数与密度$\varrho$乘以Levi-Civita符号的微分多项式。我们将旧顶点分解为子图，使得每个新的内顶点包含一个Casimir或一个Levi-Civita符号${}\times\varrho$。利用这种微图演算，我们证明Kontsevich的四面体$γ_3$-流在$\mathbb{R}^3$上Nambu-行列式Poisson括号空间中是一个Poisson上边缘：我们用微图实现了$\smash{\vec{X}}$这个平凡化向量场。该$\smash{\vec{X}}$投影到$\smash{\mathbb{R}^2}$上已知的$γ_3$-流平凡化向量场。
英文摘要：
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${}\times\varrho$. Using this micro-graph calculus, we show that Kontsevich's tetrahedral $γ_3$-flow on the space of Nambu-determinant Poisson brackets over $\mathbb{R}^3$ is a Poisson coboundary: we realize the trivializing vector field $\smash{\vec{X}}$ over $\smash{\mathbb{R}^3}$ using micro-graphs. This $\smash{\vec{X}}$ projects to the known trivializing vector field for the $γ_3$-flow over $\smash{\mathbb{R}^2}$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
