Perverse equivalences, BB-tilting, mutations and applications

Abstract

We relate the notions of BB-tilting and perverse derived equivalence at a vertex. Based on these notions, we define mutations of algebras, leading to derived equivalent ones. We present applications to endomorphism algebras of cluster-tilting objects in 2-Calabi-Yau categories and to algebras of global dimension at most 2.

26 pages

References in corpus (11)

• On triangulated orbit categories
• Cluster structures for 2-Calabi-Yau categories and unipotent groups
• Auslander correspondence
• Deformed Calabi-Yau Completions
• Mutation classes of \tilde{A}_n-quivers and derived equivalence classification of cluster tilted algebras of type \tilde{A}_n
• Towards derived equivalence classification of the cluster-tilted algebras of Dynkin type D
• Stable categories of higher preprojective algebras
• Derived equivalences from mutations of quivers with potential
• Derived equivalence classification of m-cluster tilted algebras of type A
• Derived classification of gentle algebras with two cycles
• Almost $\mathcal{D}$-split sequences and derived equivalences

Cited by in corpus (15)

• Towards derived equivalence classification of the cluster-tilted algebras of Dynkin type D
• Stable categories of higher preprojective algebras
• Mutation classes of certain quivers with potentials as derived equivalence classes
• Derived equivalence classification of the cluster-tilted algebras of Dynkin type E
• Algebras of quasi-quaternion type
• Derived equivalences from cohomological approximations, and mutations of $\Phi$-Yoneda algebras
• From groups to clusters
• Cohen-Macaulay Auslander algebras of gentle algebras
• Counting using Hall Algebras III. Quivers with Potentials
• On mutations of selfinjective quivers with potential
• Derived equivalences in n-angulated categories
• Endomorphism algebras of maximal rigid objects in cluster tubes
• The singularity categories of the Cluster-tilted algebras of Dynkin type
• APR tilting modules and graded quivers with potential
• Symmetric approximation sequences, Beilinson-Green algebras and derived equivalences