Exotic cluster structures on SL5

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A conjecture by Gekhtman, Shapiro and Vainshtein suggests a correspondence between the Belavin-Drinfeld (BD) classification of solutions of the classical Yang-Baxter equation and cluster structures on simple Lie groups. This paper confirms the conjecture for SL5. Given a BD class, we construct the corresponding cluster structure in script O sign(SL5), and show that it satisfies all parts of the conjecture.

Original languageEnglish
Article number474002
JournalJournal of Physics A: Mathematical and Theoretical
Issue number47
StatePublished - 28 Nov 2014

Bibliographical note

Publisher Copyright:
© 2014 IOP Publishing Ltd.


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

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modeling and Simulation
  • Mathematical Physics
  • General Physics and Astronomy


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