Poisson-Lie T-Duality and non trivial monodromies

Abstract We describe a general framework for studying duality among different phase spaces which share the same symmetry group H . Solutions corresponding to collective dynamics become dual in the sense that they are generated by the same curve in H . Explicit examples of phase spaces which are dual with respect to a common non-trivial coadjoint orbit O c , 0 ( α , 1 ) ⊂ h ∗ are constructed on the cotangent bundles of the factors of a double Lie group H = N ⋈ N ∗ . In the case H = L D , the loop group of a Drinfeld double Lie group D , we built up a hamiltonian description of Poisson–Lie T -duality for non-trivial monodromies and its relation with non-trivial coadjoint orbits is obtained.