论文标题
气缸上的非交通网络
Noncommutative Networks on a Cylinder
论文作者
论文摘要
在本文中，从范登·伯格（Van den Bergh）的意义上讲，双重的准泊松支架是建立在嵌入磁盘或圆柱体$σ$弧形的非交换权重的空间上基于$ p \ in \partialς$的表面的基本组。该支架还诱导了一个非交换性的高盛泊松支架，在循环空间$ \ mathcal c_ \ natural $上，这是一个$ \ mathbf k $ - 未铺设环的空间。我们表明，可以通过非交换性$ r $ -matrix形式主义来描述边界测量之间诱导的双准泊松支架。这为N. ovenhouse的结果提供了更概念性的证明，该结果的痕迹痕迹构成了无限共同的汉密尔顿人的无限集合，这是关于$ \ Mathcal c_ \ natural $的非交通性高盛。
In this paper a double quasi Poisson bracket in the sense of Van den Bergh is constructed on the space of noncommutative weights of arcs of a directed graph embedded in a disk or cylinder $Σ$, which gives rise to the quasi Poisson bracket of G.Massuyeau and V.Turaev on the group algebra $\mathbf kπ_1(Σ,p)$ of the fundamental group of a surface based at $p\in\partialΣ$. This bracket also induces a noncommutative Goldman Poisson bracket on the cyclic space $\mathcal C_\natural$, which is a $\mathbf k$-linear space of unbased loops. We show that the induced double quasi Poisson bracket between boundary measurements can be described via noncommutative $r$-matrix formalism. This gives a more conceptual proof of the result of N. Ovenhouse that traces of powers of Lax matrix form an infinite collection of noncommutative Hamiltonians in involution with respect to noncommutative Goldman bracket on $\mathcal C_\natural$.
