Maximal Commutative Subalgebras Invariant for CP-Maps:   (Counter-)Examples
  We solve, mainly by counterexamples, many natural questions regarding maximal commutative subalgebras invariant under CP-maps or semigroups of CP-maps on a von Neumann algebra. In particular, we discuss the structure of the generators of norm continuous semigroups on B(G) leaving a maximal commutative subalgebra invariant and show that there exists Markov CP-semigroups on M_d without invariant maximal commutative subalgebras for any d>2. 
B.V.Rajarama Bhat, Franco Fagnola, Michael Skeide