  Poisson-Lie duality is a generalization of abelian and non-abelian T-duality,
and it can be viewed as a map between solutions of the low-energy effective
equations of string theory, i.e. at the (super)gravity level. We show that this
fact extends to the next order in $\alpha'$ (two loops in $\sigma$-model
perturbation theory) provided that the map is corrected. The
$\alpha'$-correction to the map is induced by the anomalous Lorentz
transformations of the fields that are necessary to go from a doubled
$O(D,D)$-covariant formulation to the usual (super)gravity description.
