DUAL NON-ABELIAN DUALITY AND THE DRINFELD DOUBLE

The standard notion of the non-Abelian duality in string theory is gen eralized to the class of sigma-models admitting a Poisson-Lie-like sym metry. Such sigma-models can be associated with every Lie bialgebra (G ,G). Within the enlarged class of the backgrounds the non-Abelian dual ity is a duality transformation in the proper sense of the word. It ex changes the roles of G and G and it can be interpreted as a symplectom orphism of the phase spaces of the mutually dual theories. We give exp licit formulas for the non-Abelian duality transformation for any (G,G ). The non-Abelian analogue of the Abelian modular space O(d,d;Z) cons ists of all maximally isotropic decompositions of the corresponding Dr infeId double.