  The dynamical-algebraic structure underlying all the schemes for quantum
information stabilization is argued to be fully contained in the reducibility
of the operator algebra describing the interaction with the environment of the
coding quantum system. This property amounts to the existence of a non-trivial
group of symmetries for the global dynamics. We provide a unified framework
which allows us to build systematically new classes of error correcting codes
and noiseless subsystems. It is shown how by using symmetrization strategies
one can artificially produce noiseless subsystems supporting universal quantum
computation.
