Brauer graph algebras are closed under derived equivalence

TL;DR

This paper proves that Brauer graph algebras remain within their class when subjected to derived equivalences, using automorphism group properties to establish this closure.

Contribution

It introduces a novel approach using the rank of the maximal torus of outer automorphisms to prove closure under derived equivalence for Brauer graph algebras.

Findings

Brauer graph algebras are closed under derived equivalence.

Automorphism group properties are key to the proof.

The method applies to symmetric stably biserial algebras.

Abstract

In this paper the class of Brauer graph algebras is proved to be closed under derived equivalence. For that we use the rank of the maximal torus of the identity component $Out^0(A)$ of the group of outer automorphisms of a symmetric stably biserial algebra $A$.