Tilting mutations as generalized Kauer moves for (skew) Brauer graph algebras with multiplicity

TL;DR

This paper extends the concept of generalized Kauer moves to skew Brauer graph algebras with arbitrary multiplicity, demonstrating they induce derived equivalences via tilting mutations and linking skew Brauer graph algebras to skew gentle algebras.

Contribution

It generalizes Kauer moves to broader classes of Brauer graph algebras and establishes their role in derived equivalences through tilting mutations.

Findings

Generalized Kauer moves induce derived equivalences in skew Brauer graph algebras.

Skew Brauer graph algebras of multiplicity 1 are trivial extensions of skew gentle algebras.

The paper extends known results to more general algebraic structures.

Abstract

Generalized Kauer moves are local moves of multiple edges in a Brauer graph that yield derived equivalences between Brauer graph algebras of multiplicity identically 1. Moreover, these derived equivalences are given by a tilting mutation. The goal of this paper is to generalize this result first for Brauer graph algebras with arbitrary multiplicity and second for a generalization of Brauer graph algebras called skew Brauer graph algebras. In these contexts, we prove that the generalized Kauer moves induce derived equivalences via tilting mutations. We also show that skew Brauer graph algebras of multiplicity identically 1 can be seen as the trivial extension of skew gentle algebras.