Time-dependent invariants of motion for complete sets of non-commuting observables

Using the generalized Ehrenfest theorem the dynamics of the mean values of a complete set of non-commuting observables (CSNCO) associated to a given Hamiltonian is expressed. We found refined time-dependent invariants of motion (TDIM) for the CSNCO, and associated them with different Lie algebras. We also show that when the CSNCO are related through an antisymmetric matrix, then the characteristic polynomial of the covariance matrix for the CSNCO is also a TDIM. Examples for the Heisemberg, SU(2) and SO(2) groups are outlined.