Group actions and coverings of Brauer graph algebras

TL;DR

This paper develops a theory of group actions and coverings on Brauer graphs, showing how any Brauer graph can be systematically covered to simplify its structure and classifying certain coverings of Brauer graph algebras.

Contribution

It introduces a framework for group actions and coverings on Brauer graphs and classifies coverings that preserve Brauer graph algebra structure.

Findings

Any Brauer graph can be covered by a tower with simplified properties.

Classified coverings of Brauer graph algebras that remain within the same algebra class.

Abstract

We develop a theory of group actions and coverings on Brauer graphs that parallels the theory of group actions and coverings of algebras. In particular, we show that any Brauer graph can be covered by a tower of coverings of Brauer graphs such that the topmost covering has multiplicity function identically one, no loops, and no multiple edges. Furthermore, we classify the coverings of Brauer graph algebras that are again Brauer graph algebras.