论文标题
$ \ mathbb {r}^{d} $上的Nambu-Poisson结构的Kontsevich塔的变形塔。
The tower of Kontsevich deformations for Nambu-Poisson structures on $\mathbb{R}^{d}$: dimension-specific micro-graph calculus
论文作者
论文摘要
在Kontsevich的图表演算中，有向图的内部顶点由多向量（例如泊松双向量）居住。 nambu确定的泊松支架是卡西米尔（S）和密度$ \ varrho $ times levi-civita符号的差异化聚体。我们将旧顶点解析到子图中，以便每个新的内部顶点都包含一个Casimir或一个Levi-Civita符号$ {} \ times \ times \ varrho $。使用此微图子演算，我们表明Kontsevich的四面体$γ_3$ - 流在Nambu确定的泊松托架上$ \ Mathbb {r}^3 $是Poisson cobound，是一个poisson coboundary：我们意识到毫无用处：我们意识到毫无用处$ \ smash {\ mathbb {r}^3} $使用微图。此$ \ smash {\ vec {x}} $项目$ \ \ smash {\ mathbb {r}^2} $ of $γ_3$ -Flow的已知琐事矢量字段。
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 $\smash{\mathbb{R}^2}$.
