Poisson-Lie T-duality for quasitriangular Lie bialgebras

We introduce a new 2-parameter family of sigma models exhibiting Poisson-Li e T-duality on a quasitriangular Poisson-Lie group G. The models contain pr eviously known models as well as a new 1-parameter line of models having th e novel feature that the Lagrangian takes the simple form L = E(u(-1)u(+), u(-1)u(-)), where the generalised metric E is constant (not dependent on th e field EI as in previous models). We characterise these models in terms of a global conserved G-invariance. The models on G = SU2 and its dual G* are computed explicitly. The general theory of Poisson-Lie T-duality is also e xtended, notably the reduction of the Hamiltonian formulation to constant l oops as integrable motion on the group manifold. The approach also points i n principle to the extension of T-duality in the Hamiltonian formulation to group factorisations D = G X M, where the subgroups need not be dual or co nnected to the Drinfeld double.