On the generators of quantum dynamical semigroups with invariant subalgebras

摘要: The problem of characterizing GKLS-generators and CP-maps with an invariant von Neumann algebra appeared in different guises in the literature. We prove two unifying results, which hold even for weakly closed *-algebras: first, we show how to construct a normal form for -invariant GKLS-generators, if a normal form for -invariant CP-maps is known — rendering the two problems essentially equivalent. Second, we provide a normal form for -invariant CP-maps if is atomic (which includes the finite-dimensional case). As an application we reproduce several results from the literature as direct consequences of our characterizations and thereby point out connections between different fields.