Compatibility of Poisson-Lie transformations and symmetries of generalized supergravity equations

We investigate two types of transformations that keep NS-NS generalized supergravity equations satisfied: chi-symmetry (20) that shifts dilaton and gauge transformations (30) that change both dilaton and vector field J. Due to these symmetries there is a large set of dilatons and vector fields J that (for a fixed metric and B-field) satisfy generalized supergravity equations but only some of them can be be used as input for Poisson-Lie transformations. Conditions that define the admissible dilatons are given and examples are presented.