  Let ${\cal H}$ be the state-space of a quantum computer coupled with the
environment by a set of error operators spanning a Lie algebra ${\cal L}.$
Suppose ${\cal L}$ admits a noiseless quantum code i.e., a subspace ${\cal
C}\subset{\cal H}$ annihilated by ${\cal L}.$ We show that a universal set of
gates over $\cal C$ is obtained by any generic pair of ${\cal L}$-invariant
gates. Such gates - if not available from the outset - can be obtained by
resorting to a symmetrization with respect to the group generated by ${\cal
L}.$ Any computation can then be performed completely within the coding
decoherence-free subspace.
