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Four-dimensional Manin triples and Drinfeld doubles are classified andcorresponding two-dimensional Poisson-Lie T-dual sigma models on them areconstructed. The simplest example of a Drinfeld double allowing decompositioninto two nontrivially different Manin triples is presented.Comment: 6 pages, LaTeX; correction: two Manin triples originally considered  separately are shown to lead to the same Drinfeld doubl

CLASSIFICATION OF POISSON–LIE T-DUAL MODELS WITH TWO-DIMENSIONAL TARGETS