2002/08/05 by M. Gekhtman, M. Shapiro, Gekhtman, M. +5 · 10 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA) #Symplectic Geometry (math.SG) #math.AG #math.CO #math.QA #math.SG
paper · pdf · doi:10.48550/arxiv.math/0208033
minor changes
openalex publication_date 2002/08/05 · arxiv created 2003/11/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.