Cluster structures on simple complex lie groups and Belavin-Drinfeld classification

M. Gekhtman, M. Shapiro, A. Vainshtein

Research output: Contribution to journalArticlepeer-review


We study 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 G corresponds to a cluster structure in O(G). We prove a reduction theorem explaining how different parts of the conjecture are related to each other. The conjecture is established for SLn, n < 5, and for any G in the case of the standard Poisson-Lie structure.

Original languageEnglish
Pages (from-to)293-312
Number of pages20
JournalMoscow Mathematical Journal
Issue number2
StatePublished - 2012


  • Belavin-Drin-feld triple
  • Cluster algebra
  • Poisson-Lie group

ASJC Scopus subject areas

  • General Mathematics


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