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Local Poisson groupoids over mixed product Poisson structures and generalised double Bruhat cells
Victor Mouquin
Given a standard complex semisimple Poisson Lie group , generalised double Bruhat cells and generalised Bruhat cells equipped with naturally defined h…
The Fock-Rosly Poisson Structure as Defined by a Quasi-Triangular -Matrix
Victor Mouquin
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 al…
Double Bruhat cells and symplectic groupoids
Jiang-Hua Lu, Victor Mouquin
Let be a connected complex semisimple Lie group, equipped with a standard multiplicative Poisson structure determined by a pair of opposite Borel subgroups $(B, B_…
On the T-leaves of some Poisson structures related to products of flag varieties
Jiang-Hua Lu, Victor Mouquin
For a connected abelian Lie group T acting on a Poisson manifold (Y,π) by Poisson isomorphisms, the T-leaves of π in Y are, by definition, the orbits of the symplectic leaves of π…
Mixed product Poisson structures associated to Poisson Lie groups and Lie bialgebras
Jiang-Hua Lu, Victor Mouquin
We introduce and study some mixed product Poisson structures on product manifolds associated to Poisson Lie groups and Lie bialgebras. For quasitriangular Lie bialgebras, our const…