  In the present work we review and refine some results about fixed points of
semigroups of quantum channels. Noncommutative potential theory enables us to
show that the set of fixed points of a recurrent semigroup is a W*-algebra;
aside from the intrinsic interest of this result, it brings an improvement in
the study of fixed points by means of absorption operators (a noncommutative
generalization of absorption probabilities): under the assumption of absorbing
recurrent space (hence allowing non-trivial transient space) we can provide a
description of the fixed points set and a probabilistic characterization of
when it is a W*-algebra in terms of absorption operators. Moreover we are able
to exhibit an example of a recurrent semigroup which does not admit a
decomposition of the Hilbert space into orthogonal minimal invariant domains
(contrarily to the case of classical Markov chains and positive recurrent
semigroups of quantum channels).
