Generalized cluster structure on the Drinfeld double of $G{L}_n$

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 dual Poisson--Lie bracket.

arXiv commentThis is a short announcement. The proofs will be published in a subsequent paper. Version 2: several misprints are corrected