Mutations Vs. Seiberg duality

TL;DR

This paper compares mutations and Seiberg duality in quivers with potentials, showing they coincide for certain classes and thus produce derived equivalent algebras, linking combinatorial and algebraic dualities.

Contribution

It establishes the equivalence of mutations and Seiberg duality for a class of potentials, connecting combinatorial and algebraic approaches in quiver theory.

Findings

Mutations coincide with Seiberg duality for good potentials.

Mutations produce derived equivalent algebras.

The work bridges combinatorial and algebraic dualities.

Abstract

For a quiver with potential, Derksen, Weyman and Zelevinsky defined a combinatorial transformation - mutations. Mukhopadhyay and Ray, on the other hand, tell us how to compute Seiberg dual quivers for some quivers with potentials through a tilting procedure, thus obtaining derived equivalent algebras. In this text, we compare mutations with the concept of Seiberg duality, concluding that for a certain class of potentials (the good ones) mutations coincide with Seiberg duality, therefore giving derived equivalences.