  Starting from the classification of 6-dimensional Drinfeld doubles and their
decomposition into Manin triples we construct 3-dimensional Poisson-Lie T-dual
or more precisely T-plural sigma models. Of special interest are those that are
conformally invariant. Examples of models that satisfy vanishing beta-function
equations with zero dilaton are presented and their duals are calculated. It
turns out that for "traceless" dual algebras they satisfy the beta-function
equations as well but usually with rather nontrivial dilaton. We also present
explicit examples of several kinds of obstacles and difficulties present in
construction of quantum dual models. Such concrete examples might be helpful in
further development and improvement of quantum version of Poisson-Lie
T-duality.
