Introduction: Exotic cluster structures on SLn: The cremmer-gervais case

M. Gekhtman, M. Shapiro, A. Vainshtein

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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 G corresponds to a cluster structure in O(G). We have shown before that this conjecture holds for any G in the case of the standard Poisson-Lie structure and for all Belavin-Drinfeld classes in SLn, n < 5. In this paper we establish it for the Cremmer-Gervais Poisson-Lie structure on SLn, which is the least similar to the standard one.

Original languageEnglish
Pages (from-to)1-106
Number of pages106
JournalMemoirs of the American Mathematical Society
Issue number1165
StatePublished - Mar 2017

Bibliographical note

Publisher Copyright:
© 2016 American Mathematical Society.


  • Belavin-Drinfeld triple
  • Cluster algebra
  • Poisson-Lie group

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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