On mutations of selfinjective quivers with potential

TL;DR

This paper explores the relationship between silting mutations and quiver with potential mutations in selfinjective algebras, establishing compatibility and deriving new equivalences of Jacobian algebras.

Contribution

It demonstrates that silting mutation is compatible with QP mutation and provides a family of derived equivalences for Jacobian algebras.

Findings

Silting mutation is compatible with QP mutation.

Derived equivalences of Jacobian algebras are established.

Provides a framework linking mutations and derived categories.

Abstract

We study silting mutations (Okuyama-Rickard complexes) for selfinjective algebras given by quivers with potential (QPs). We show that silting mutation is compatible with QP mutation. As an application, we get a family of derived equivalences of Jacobian algebras.