Covariant Uniformly Continuous Quantum Markov Semigroups

Abstract

In this paper we analyze the structure of decoherence-free subalgebra N(T) of a uniformly continuous covariant semigroup with respect to a representation π of a compact group G on h. In particular, we 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. We extend this result when π is reducible and N(T) is atomic by the decomposition of h due to the Peter–Weyl theorem.