Abstract
It is well known that Brauer graph algebras coincide with symmetric special biserial algebras and there has been a lot of work on Brauer graph algebras and their representation theory. Given a Brauer graph algebra A associated with a Brauer graph G, we denote by gr(A) the graded algebra associated with the radical filtration of A. We give a criterion for gr(A) to be representation-finite in terms of the graded degrees of vertices in G. Moreover, when gr(A) is representation-finite, we give the precise relationship between the Auslander–Reiten quiver of A and the Auslander–Reiten quiver of gr(A).
Acknowledgments
We would like to thank Yu Ye and Steffen Koenig for their comments and suggestions on a previous version of this article. We would like to thank an anonymous referee for careful reading and many constructive suggestions, which have led to substantial changes and significant improvement on the presentation of this article.