论文标题
Kontsevich的明星产品升至7次，用于Aggine Poisson Brackets：Riemann Zeta值在哪里？
Kontsevich's star-product up to order 7 for affine Poisson brackets: where are the Riemann zeta values?
论文作者
论文摘要
Kontsevich Star-Product承认了对仿期类别的定义明确的限制，特别是线性 - 泊松支架；它的图形扩展仅由Kontsevich的图形组成，其级别$ \ leqslant 1 $用于航空顶点。我们获得了公式$ \ star _ {\ text {aff}} \ text {mod} \ bar {o}（\ hbar^7）$带有谐波繁殖器的图形权重（超过$ n \ leqslant 7 $ aerial Vertices）;我们验证所有这些重量都满足了Shoikhet的循环重量关系 - Felder-willwacher，它们使用Panzer使用$ \ textsf {Kontsevint} $软件匹配计算，并且由此产生的offine star-product是coopiative modulo modulo $ \ bar $ \ bar {o} o}（o}（O}（O}（O}（\ Hbar^7）$。 我们发现，Riemann Zeta值$ζ（3）^2/π^6 $，它进入谐波图（最多为理由），实际上从$ \ star _ {\ star _ {\ text {aff}}} \ text {aff}} \ text {mod} {mod} {mod} \ bar {o}（o} $}的分析公式中消失了$ \ mathbb {q} $ - kontsevich图的线性组合附近$ζ（3）^2/π^6 $代表了雅各比身份的差异后果，因此仿射泊松支架的贡献消失了。因此，我们得出了一个即时使用的较短公式$ \ star _ {\ text {aff}}^{\ text {red}} $ mod〜 $〜$ \ bar {o}（\ hbar^7）$，只有合理系数。
The Kontsevich star-product admits a well-defined restriction to the class of affine -- in particular, linear -- Poisson brackets; its graph expansion consists only of Kontsevich's graphs with in-degree $\leqslant 1$ for aerial vertices. We obtain the formula $\star_{\text{aff}}\text{ mod }\bar{o}(\hbar^7)$ with harmonic propagators for the graph weights (over $n\leqslant 7$ aerial vertices); we verify that all these weights satisfy the cyclic weight relations by Shoikhet--Felder--Willwacher, that they match the computations using the $\textsf{kontsevint}$ software by Panzer, and the resulting affine star-product is associative modulo $\bar{o}(\hbar^7)$. We discover that the Riemann zeta value $ζ(3)^2/π^6$, which enters the harmonic graph weights (up to rationals), actually disappears from the analytic formula of $\star_{\text{aff}}\text{ mod }\bar{o}(\hbar^7)$ \textit{because} all the $\mathbb{Q}$-linear combinations of Kontsevich graphs near $ζ(3)^2/π^6$ represent differential consequences of the Jacobi identity for the affine Poisson bracket, hence their contribution vanishes. We thus derive a ready-to-use shorter formula $\star_{\text{aff}}^{\text{red}}$ mod~$\bar{o}(\hbar^7)$ with only rational coefficients.
