Structure of covariant uniformly continuous Quantum Markov Semigroups

In this thesis I analyze the structure of decoherence-free subalgebra N(T) of a uniformly continuous covariant Quantum Markov Semigroup (QMS) with respect to a representation π of a compact group G on a Hilbert space h. In particular, I obtain that, when π is irreducible, N(T) is isomorphic to (ℬ(k) ⊗ 1m)^d for suitable Hilbert spaces k and m, and an integer d related to the connected components of G. I extend this result when π is reducible and N(T) is atomic by the decomposition of h due to the Peter–Weyl theorem. The thesis is then concluded by exploring the possibility of extending these results beyond the direct sum by using the concept of direct integral.