  The problem of characterizing GKLS-generators and CP-maps with an invariant
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 $\mathcal{A}$-invariant GKLS-generators, if a normal form for
$\mathcal{A}$-invariant CP-maps is known - rendering the two problems
essentially equivalent. Second, we provide a normal form for
$\mathcal{A}$-invariant CP-maps if $\mathcal{A}$ 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.
