Towards derived equivalence classification of the cluster-tilted algebras of Dynkin type D

We provide a far reaching derived equivalence classification of the cluster-tilted algebras of Dynkin type D and suggest standard forms for the derived equivalence classes. We believe that the classification is complete, but some subtle questions remain open. We introduce another notion of equivalence called good mutation equivalence which is slightly stronger than derived equivalence but is algorithmically more tractable, and give a complete classification together with standard forms.