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

Symmetry Integrability and Geometry-Methods and Applications

article

Victor Mouquin¹ 

[1] University of Toronto

关键词: flat connections;    Poisson Lie groups;    r-matrices;    quasi-Poisson spaces;   

DOI  :  10.3842/SIGMA.2017.063

来源: National Academy of Science of Ukraine

【 摘 要 】

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 associated to pairs of Poisson actions, which were studied by J.-H. Lu and the author. The Fock-Rosly Poisson structure corresponds to the quasi-Poisson structure studied by Massuyeau, Turaev, Li-Bland, and Ševera under an equivalence of categories between Poisson and quasi-Poisson spaces.

【 授权许可】

Unknown