Quasi-invariance and central extensions

Motivated by the theory of anomalies, the theory of classical dynamical systems described by quasi-invariant Lagrangians is reexamined in the present paper. A mathematical structure similar to the one describing anomalies in quantum field theory is found in systems for which an invariant Lagrangian description requires central extensions of the symmetry groups of the equations of motion. The case in which the symmetry group does not allow for nontrivial central extensions is also discussed.