Mathematical Surveys and Monographs - Cluster Algebras and Poisson Geometry
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Published By American Mathematical Society

9780821849729, 9781470413941
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Pre-symplectic structures compatible with the cluster algebra structure

2010 ◽  
pp. 111-131
Author(s):  
Michael Gekhtman ◽  
Michael Shapiro ◽  
Alek Vainshtein
Keyword(s):  
Cluster Algebra ◽  
Algebra Structure ◽  
Symplectic Structures

Poisson structures compatible with the cluster algebra structure

2010 ◽  
pp. 67-99
Author(s):  
Michael Gekhtman ◽  
Michael Shapiro ◽  
Alek Vainshtein
Keyword(s):  
Cluster Algebra ◽  
Algebra Structure ◽  
Poisson Structures

Cluster algebras

2010 ◽  
pp. 37-65 ◽  
Author(s):  
Michael Gekhtman ◽  
Michael Shapiro ◽  
Alek Vainshtein
Keyword(s):  
Cluster Algebras

Perfect planar networks in a disk and Grassmannians

2010 ◽  
pp. 141-173
Author(s):  
Michael Gekhtman ◽  
Michael Shapiro ◽  
Alek Vainshtein
Keyword(s):  
Planar Networks

On the properties of the exchange graph

2010 ◽  
pp. 133-139
Author(s):  
Michael Gekhtman ◽  
Michael Shapiro ◽  
Alek Vainshtein
Keyword(s):  
Exchange Graph

The cluster manifold

2010 ◽  
pp. 101-110
Author(s):  
Michael Gekhtman ◽  
Michael Shapiro ◽  
Alek Vainshtein

Preliminaries

2010 ◽  
pp. 1-13
Author(s):  
Michael Gekhtman ◽  
Michael Shapiro ◽  
Alek Vainshtein

Generalized Bäcklund-Darboux transforms for Coxeter-Toda flows from a cluster algebra perspective

2010 ◽  
pp. 199-238
Author(s):  
Michael Gekhtman ◽  
Michael Shapiro ◽  
Alek Vainshtein
Keyword(s):  
Cluster Algebra ◽  
Darboux Transforms

Perfect planar networks in an annulus and rational loops in Grassmannians

2010 ◽  
pp. 175-197
Author(s):  
Michael Gekhtman ◽  
Michael Shapiro ◽  
Alek Vainshtein
Keyword(s):  
Planar Networks

Basic examples: Rings of functions on Schubert varieties

2010 ◽  
pp. 15-36
Author(s):  
Michael Gekhtman ◽  
Michael Shapiro ◽  
Alek Vainshtein
Keyword(s):  
Schubert Varieties
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