CLUSTER ALGEBRAS AND POISSON GEOMETRY

被引：154

作者：

Gekhtman, Michael ^{[1
]}

Shapiro, Michael ^{[2
,3
]}

Vainshtein, Alek ^{[4
,5
]}

机构：

[1] Univ Notre Dame, Dept Math, Notre Dame, IN 46556 USA

[2] KTH, Inst Matemat, Stockholm, Sweden

[3] Michigan State Univ, Dept Math, E Lansing, MI 48824 USA

[4] Univ Haifa, Dept Math, IL-31905 Haifa, Israel

[5] Univ Haifa, Dept Comp Sci, IL-31905 Haifa, Israel

来源：

MOSCOW MATHEMATICAL JOURNAL | 2003年 / 3卷 / 03期

关键词：

Cluster algebras; Poisson brackets; toric action; symplectic leaves; real Grassmannians; Sklyanin bracket;

D O I：

10.17323/1609-4514-2003-3-3-899-934

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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 R.

引用

页码：899 / 934

页数：36

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