Drinfeld double of $G{L}_n$ and generalized cluster structures

Abstract

We construct a generalized cluster structure compatible with the Poisson bracket on the Drinfeld double of the standard Poisson-Lie group $G{L}_n$ and derive from it a generalized cluster structure on $G{L}_n$ compatible with the push-forward of the Poisson bracket on the dual Poisson--Lie group.

60 pages, 9 figures, extended version of arXiv: 1507.00452; final version; presentation clarified, Remark 2.2 added, several references added

References in corpus (2)

• Cremmer--Gervais cluster structure on $S{L}_n$
• Exotic cluster structures on $S{L}_n$: the Cremmer-Gervais case

Cited by in corpus (6)

• Superintegrable Systems on Moduli Spaces of Flat Connections
• Periodic staircase matrices and generalized cluster structures
• Multiple generalized cluster structures on $D({\text{GL}}_n)$
• Generalized Cluster Structures Related to the Drinfeld Double of $G{L}_n$
• Multiple rational normal forms in Lie theory
• Starfish lemma via birational quasi-isomorphisms