COVARIANT UNIFORMLY CONTINUOUS QUANTUM MARKOV SEMIGROUPS

In this paper we analyze the structure of decoherence-free subalgebra N(T) of a uniformly continuous covariant semigroup with respect to a representation pi of a compact group G on h. In particular, we obtain that, when pi is irreducible, N(T) is isomorphic to (B(k) circle times 1(m))(d) for suitable Hilbert spaces k and m, and an integer d related to the connected components of G. We extend this result when pi is reducible and N(T) is atomic by the decomposition of h due to the Peter-Weyl theorem.