Derived equivalences from mutations of quivers with potential

TL;DR

This paper demonstrates that mutations of quivers with potential induce equivalences in 3-Calabi-Yau categories, connecting various approaches and extending previous results in the field.

Contribution

It establishes a new link between quiver mutations and derived category equivalences, improving upon prior work and relating to multiple existing theories.

Findings

Mutations induce equivalences of 3-Calabi-Yau categories.

Connects Iyama-Reiten and Koszul dual approaches.

Extends previous results by Vitoria.

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.