Poisson-Lie T-Duality and non trivial monodromies

A. CABRERA; H. MONTANI; M. ZUCCALLI

JOURNAL OF GEOMETRY AND PHYSICS

Elsevier B. V.

Año: 2009 vol. 59 p. 576 - 599

0393-0440

We describe a general framework for studying duality between different phasespaces which share the same symmetry group $mathrm{H}$. Solutionscorresponding to collective dynamics become dual in the sense that they aregenerated by the same curve in $mathrm{H}$. Explicit examples of phase spaceswhich are dual with respect to a common non trivial coadjoint orbit$mathcal{O}_{c,0}left(  mathbf{alpha},1 ight)  subsetmathfrak{h}^{ast}$ are constructed on the cotangent bundles of the factors of a double Liegroup $mathrm{H}=mathrm{N}Joinmathrm{N}^{ast}$. In the case$mathrm{H}=LD$, the loop group of a Drinfeld double Lie group $D$, ahamiltonian description of Poisson-Lie T-duality for non trivial monodromiesand its relation with non trivial coadjoint orbits is obtained.