Cluster algebras and Poisson geometry
量子代数
2007-05-23 v2 代数几何
组合数学
辛几何
摘要
We introduce a Poisson variety compatible with a cluster algebra structure and a compatible toric action on this variety. We study Poisson and topological properties of the union of generic orbits of this toric action. In particular, we compute the number of connected components of the union of generic toric orbits for cluster algebras over real numbers. As a corollary we compute the number of connected components of refined open Bruhat cells in Grassmanians G(k,n) over real numbers.
引用
@article{arxiv.math/0208033,
title = {Cluster algebras and Poisson geometry},
author = {M. Gekhtman and M. Shapiro and A. Vainshtein},
journal= {arXiv preprint arXiv:math/0208033},
year = {2007}
}
备注
minor changes