再论Kontsevich四面体流
The Kontsevich tetrahedral flow revisited
摘要：
证明了Kontsevich四面体流$\dot{\mathcal{P}} = \mathcal{Q}_{a:b} (\mathcal{P})$，其右端是仿射实Poisson流形$N^n$上的双向量$\mathcal{P}$中的两个四次微分单项式的线性组合，无穷小地保持$N^n$上Poisson双向量空间的充要条件是$\mathcal{Q}_{a:b} (\mathcal{P})$中的两个单项式由比率$a:b=1:6$平衡.证明是明确的;它是写在语言的Kontsevich图。
英文摘要：
We prove that the Kontsevich tetrahedral flow $\dot{\mathcal{P}} = \mathcal{Q}_{a:b} (\mathcal{P})$, the right-hand side of which is a linear combination of two differential monomials of degree four in a bi-vector $\mathcal{P}$ on an affine real Poisson manifold $N^n$, does infinitesimally preserve the space of Poisson bi-vectors on $N^n$ if and only if the two monomials in $\mathcal{Q}_{a:b} (\mathcal{P})$ are balanced by the ratio $a:b=1:6$. The proof is explicit; it is written in the language of Kontsevich graphs.
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