Brauer graph algebras are defined by combinatorial data based on graphs:

Underlying every Brauer graph algebra is a finite graph, the Brauer graph, equipped with with a cyclic orientation of the edges at every vertex and a multiplicity function. This combinatorial data encodes much of the representation theory of Brauer graph algebras and is part of the reason for the ongoing interest in this class of algebras. A known result by Schroll states that Brauer graph algebras, with multiplicity function one, give rise to all possible trivial extensions for gentle algebras. On the other hand, Geiss and de la Peña studied a generalization of gentle algebras called skew-gentle algebras.

In our ongoing project we establish the right definition of skew-Brauer graph algebra in such a way that the result by Schroll can be enunciated in this context. That is, A is a skew-Brauer graph algebra with multiplicity function equal to one if and only if it is the trivial extension of a skew-gentle algebra. Moreover, the family of skew-Brauer graph algebras with arbitrary multiplicity function generalizes the family of Brauer graph algebras with arbitrary multiplicity function.