Classification of two-term tilting complexes over Brauer graph algebras

TL;DR

This paper classifies two-term tilting complexes over Brauer graph algebras using combinatorial methods and identifies which algebras are tilting-discrete.

Contribution

It provides a combinatorial classification of two-term tilting complexes and characterizes tilting-discrete Brauer graph algebras.

Findings

Complete classification of two-term tilting complexes

Identification of tilting-discrete Brauer graph algebras

Use of ribbon graph combinatorics

Abstract

Using only the combinatorics of its defining ribbon graph, we classify the two-term tilting complexes, as well as their indecomposable summands, of a Brauer graph algebra. As an application, we determine precisely the class of Brauer graph algebras which are tilting-discrete.