Noncentral extensions as anomalies in classical dynamical systems

A two cocycle is associated to any action of a Lie group on a symplectic manifold. This allows to enlarge the concept of anomaly in classical dynamical systems considered by F. Toppan [in J. Nonlinear Math. Phys. 8, no.3 (2001) 518-533] so as to encompass some extensions of Lie algebras related to noncanonical actions.