环上有向网络的Poisson几何
Poisson Geometry of Directed Networks in an Annulus
摘要：
作为Postnikov构造的推广（参见arXiv：math/0609764），我们定义了一个从环中有向网络的边权空间到格拉斯曼环中的环空间的映射。然后，我们表明，通用的泊松括号arXiv：0805.3541中的边权重的空间中引入诱导一个家庭的泊松结构的有理值矩阵函数和循环的空间中的格拉斯曼。在前一种情况下，对于特定类型的网络，这个族包括与三角R矩阵相关的泊松括号。
英文摘要：
As a generalization of Postnikov's construction (see arXiv: math/0609764), we define a map from the space of edge weights of a directed network in an annulus into a space of loops in the Grassmannian. We then show that universal Poisson brackets introduced for the space of edge weights in arXiv: 0805.3541 induce a family of Poisson structures on rational-valued matrix functions and on the space of loops in the Grassmannian. In the former case, this family includes, for a particular kind of networks, the Poisson bracket associated with the trigonometric R-matrix.
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