The Fock-Rosly Poisson Structure as Defined by a Quasi-Triangular r-Matrix

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2017
• Main Author: Mouquin, V.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2017
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/148752
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: The Fock-Rosly Poisson Structure as Defined by a Quasi-Triangular r-Matrix / V. Mouquin // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 10 назв. — англ.

We reformulate the Poisson structure discovered by Fock and Rosly on moduli spaces of flat connections over marked surfaces in the framework of Poisson structures defined by Lie algebra actions and quasitriangular r-matrices, and we show that it is an example of a mixed product Poisson structure ass...