Cluster algebras and Poisson geometry

Details Cluster algebras and Poisson geometry Cluster algebras and Poisson geometry

2002-08-05

arxiv.org/abs/math/0208033v2

Mathematics

Quantum Algebra

minor changes

Scientific paper

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.

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