Derived equivalences from mutations of quivers with potential

Abstract

We show that Derksen-Weyman-Zelevinsky's mutations of quivers with potential yield equivalences of suitable 3-Calabi-Yau triangulated categories. Our approach is related to that of Iyama-Reiten and Koszul dual to that of Kontsevich-Soibelman. It improves on previous work by Vitoria. In the appendix, the first-named author studies pseudo-compact derived categories of certain pseudo-compact dg algebras.

section 2.16 added, 48 pages, with an appendix by B. Keller

References in corpus (4)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Calabi-Yau algebras
• Seiberg Duality for Quiver Gauge Theories
• Quivers with potentials and their representations II: Applications to cluster algebras

Cited by in corpus (9)

• Two kinds of derived categories, Koszul duality, and comodule-contramodule correspondence
• Deformed Calabi-Yau Completions
• Perverse equivalences, BB-tilting, mutations and applications
• Towards derived equivalence classification of the cluster-tilted algebras of Dynkin type D
• Wall-crossing of the motivic Donaldson-Thomas invariants
• Derived equivalence classification of the cluster-tilted algebras of Dynkin type E
• About the Absence of Exotics and the Coulomb Branch Formula
• Mutation, Witten Index, and Quiver Invariant
• Helices on del Pezzo surfaces and tilting Calabi-Yau algebras