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.

5 Pages, Latex. Presentation improved, results unchanged. To appear in PRA