Multiple generalized cluster structures on $D({\text{GL}}_n)$

Abstract

We produce a large class of generalized cluster structures on the Drinfeld double of ${\text{GL}}_n$ that are compatible with Poisson brackets given by Belavin-Drinfeld classification. The resulting construction is compatible with the previous results on cluster structures on ${\text{GL}}_n$.

84 pages, 30 figures

References in corpus (3)

• Periodic staircase matrices and generalized cluster structures
• Generalized Cluster Structures Related to the Drinfeld Double of $G{L}_n$
• Introduction to Cluster Algebras. Chapter 6

Cited by in corpus (2)

• Multiple rational normal forms in Lie theory
• Starfish lemma via birational quasi-isomorphisms