• Corpus ID: 212736892

# Darboux coordinates for symplectic groupoid and cluster algebras

@inproceedings{LChekhov2020DarbouxCF,
title={Darboux coordinates for symplectic groupoid and cluster algebras},
author={L.Chekhov and M.Shapiro},
year={2020}
}
• Published 17 March 2020
• Mathematics
Using Fock–Goncharov higher Teichmüller space variables we derive Darboux coordinate representation for entries of general symplectic leaves of the An groupoid of uppertriangular matrices and, in a more general setting, of higher-dimensional symplectic leaves for algebras governed by the reflection equation with the trigonometric R-matrix. The obtained results are in a perfect agreement with the previously obtained Poisson and quantum representations of groupoid variables for A3 and A4 in terms…

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