Invariant Projections for Covariant Quantum Markov Semigroups

. In this paper we investigate consequences of covariance of a uni- formly Quantum Markov Semigroup, under a group action, on the structure of its minimal invariant projections. We obtain that, under suitable hypotheses, minimal invariant projections correspond to irreducible sub-representations in which the initial covariant representation is decomposed. We apply this results in the study circulant Quantum Markov Semigroups.