Michael Gekhtman's Books

The first book devoted to cluster algebras, this work contains chapters on Poisson geometry and Schubert varieties; an introduction to cluster algebras and their main properties; and geometric aspects of the cluster algebra theory, in particular on its relations to Poisson geometry and to the theory of integrable systems.

This is the second paper in the series of papers dedicated to the study of natural cluster structures in the rings of regular functions on simple complex Lie groups and Poisson–Lie structures compatible with these cluster structures. According to our main conjecture, each class in the Belavin–Drinfeld classification of Poisson–Lie structures on corresponds to a cluster structure in . The authors have shown before that this conjecture holds for any in the case of the standard Poisson–Lie structure and for all Belavin–Drinfeld classes in , . In this paper the authors establish it for the Cremmer–Gervais Poisson–Lie structure on , which is the least similar to the standard one.

Book's by Michael Gekhtman

Cluster Algebras and Poisson Geometry

Cluster Algebras and Poisson Geometry

The Strong K�nneth Theorem for Topological Periodic Cyclic Homology

The Strong K�nneth Theorem for Topological Periodic Cyclic Homology

Cluster Algebras and Poisson Geometry

Cluster Algebras and Poisson Geometry

A Plethora of Cluster Structures on $GL_n$

A Plethora of Cluster Structures on $GL_n$

Exotic Cluster Structures on $SL_n$: The Cremmer-Gervais Case

Exotic Cluster Structures on $SL_n$: The Cremmer-Gervais Case

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