# From Brauer graph algebras to biserial weighted surface algebras

## TL;DR

This paper establishes a deep connection between Brauer graph algebras and biserial weighted surface algebras, showing they are essentially the same class under certain algebraic constructions related to triangulated surfaces.

## Contribution

It proves that Brauer graph algebras are exactly the indecomposable idempotent algebras of biserial weighted surface algebras and also relate them to periodic weighted surface algebras.

## Key findings

- Brauer graph algebras coincide with indecomposable idempotent algebras of biserial weighted surface algebras
- Brauer graph algebras are idempotent algebras of periodic weighted surface algebras
- Connection between algebraic structures and triangulated surfaces established

## Abstract

We prove that the class of Brauer graph algebras coincides with the class of indecomposable idempotent algebras of biserial weighted surface algebras. These algebras are associated to triangulated surfaces with arbitrarily oriented triangles, investigated in [17] and [18]. Moreover we prove that Brauer graph algebras are idempotent algebras of periodic weighted surface algebras, investigated in [17] and [19].