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

Abstract

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.

42 pages; v2: Minor revision. Title and abstract changed, slight changes to the introduction and in the presentation of main results in Section 2

References in corpus (7)

• On triangulated orbit categories
• On Derived Equivalences of Categories of Sheaves Over Finite Posets
• Perverse equivalences, BB-tilting, mutations and applications
• On Jacobian algebras from closed surfaces
• The mutation class of $D_n$ quivers
• Derived equivalence classification of m-cluster tilted algebras of type A
• Hochschild cohomology of the cluster-tilted algebras of finite representation type

Cited by in corpus (10)

• Perverse equivalences, BB-tilting, mutations and applications
• 2-CY-tilted algebras that are not Jacobian
• Mutation classes of certain quivers with potentials as derived equivalence classes
• Which mutation classes of quivers have constant number of arrows?
• Hochschild cohomology of the cluster-tilted algebras of finite representation type
• Minimal length maximal green sequences
• Cohen-Macaulay Auslander algebras of gentle algebras
• On mutations of selfinjective quivers with potential
• The singularity categories of the Cluster-tilted algebras of Dynkin type
• Derived equivalences of self-injective 2-Calabi--Yau tilted algebras