A generalized cluster structure on $G{L}_n$ via birational Poisson maps

Misha Gekhtman, Michael Shapiro, Alek Vainshtein

In a recent work, we constructed a rational map from a simple Lie group $\mathcal{G}$ to itself that intertwines the standard Poisson--Lie structure on $\mathcal{G}$ with a Poisson h…