
SIGMA 13 (2017), 063, 13 pages arXiv:1610.01782
https://doi.org/10.3842/SIGMA.2017.063
The FockRosly Poisson Structure as Defined by a QuasiTriangular $r$Matrix
Victor Mouquin
University of Toronto, Toronto ON, Canada
Received March 26, 2017, in final form August 01, 2017; Published online August 09, 2017
Abstract
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 FockRosly Poisson structure corresponds to the quasiPoisson structure studied by Massuyeau, Turaev, LiBland, and Ševera under an equivalence of categories between Poisson and quasiPoisson spaces.
Key words:
flat connections; Poisson Lie groups; $r$matrices; quasiPoisson spaces.
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