圆环中有向网络的泊松几何
量子代数
2016-05-19 v3
摘要
作为 Postnikov 构造（见 arXiv: math/0609764）的推广，我们定义了一个从圆环中有向网络的边权空间到格拉斯曼流形中环路空间的映射。然后，我们证明在 arXiv: 0805.3541 中为边权空间引入的通用泊松括号，在有理值矩阵函数和格拉斯曼流形中的环路空间上诱导出一族泊松结构。在前一种情形中，对于特定类型的网络，这族结构包含了与三角 R-矩阵相关联的泊松括号。
引用
@article{arxiv.0901.0020,
title = {Poisson Geometry of Directed Networks in an Annulus},
author = {Michael Gekhtman and Michael Shapiro and Alek Vainshtein},
journal= {arXiv preprint arXiv:0901.0020},
year = {2016}
}
备注
28 pages, 10 figures. Theorem 4.1 in the previous version was wrong; it has been replaced by a weaker statement. As a result, the proof of Theorem 4.7 has been changed