Exotic cluster structures on $S{L}_5$

Abstract

A conjecture by Gekhtman, Shapiro and Vainshtein suggests a correspondence between the Belavin - Drinfeld classification of solutions of the classical Yang - Baxter equation and cluster structures on simple Lie groups. This paper confirms the conjecture for $S{L}_5$. Given a Belavin - Drinfeld class, we construct the corresponding cluster structure in $\mathcal{O}\left(S{L}_5\right)$, and show that it satisfies all parts of the conjecture.

arXiv admin note: text overlap with arXiv:1101.0015 by other authors

Cited by in corpus (3)

• Cremmer--Gervais cluster structure on $S{L}_n$
• Upper cluster algebras and choice of ground ring
• Multiple generalized cluster structures on $D({\text{GL}}_n)$