Dual non-Abelian duality and the Drinfeld double

The standard notion of the non-Abelian duality in string theory is generalized to the class of σ-models admitting a Poisson-Lie-like 3ymmetry. Such σ-models can be associated with every Lie bialgebra (g,G). Within the enlarged class of the backgrouds the non-Abelian duality is a duality transformation in the pacer sense of the word. It exchanges the roles of G and G and it can be interpreted as a symplectomorphism of the phase spaces of the mutually dual theories. We give explicit formulas for the non-Abelian duality transformation for any (g,G). The non-Abelian analogue of the Abelian modular space O(d, d; Z) consists of all maximally isotropic decompositions of the corresponding Drinfeld double.