Skew-Brauer graph algebras

Abstract In this work, we introduce a new class of algebras that we denominate skew-Brauer graph algebras. This class contains and generalizes the Brauer graph algebras. We establish that skew-Brauer graph algebras are symmetric and can be defined based on a Brauer graph with additional information. We show that the class of trivial extensions of skew-gentle algebras coincides with a subclass of skew-Brauer graph algebras, where the associated skew-Brauer graph has a multiplicity function identically equal to one, generalizing a result over gentle algebras. Furthermore, we characterize skew-Brauer algebras of finite representation type. Finally, we provide a geometric interpretation of cut-sets and reflections of algebras using orbifold dissections.