  In this note we discuss symplectic lifts of actions for a complete Lagrangian
fibration. Firstly, we describe the symplectic cotangent lifts of a G-action on
a manifold Q in terms of 1-cocycles in the cohomology of G induced by the
action with values in the space of closed 1-forms on Q. After this, we consider
the general case of complete Lagrangian fibrations.
