  Preservation of coherence is a fundamental yet subtle phenomenon in open
systems. We uncover its relation to symmetries respected by the system
Hamiltonian and its coupling to the environment. We discriminate between local
and global classes of decoherence-free subspaces for many-body systems through
the introduction of "ghost variables". The latter are orthogonal to the
symmetry and the coupling to the environment does not depend on them.
Constructing them is facilitated in classical phase space and can be
transferred to quantum mechanics through the equivalent role that Poisson and
Lie algebras play for symmetries in classical and quantum mechanics,
respectively. Examples are given for an interacting spin system.

Atomic Physics;Quantum Physics