Skew-Brauer graph algebras

TL;DR

This paper introduces skew-Brauer graph algebras, a new class generalizing Brauer graph algebras, with properties like symmetry, connections to skew-gentle algebras, and geometric interpretations via orbifold dissections.

Contribution

It defines skew-Brauer graph algebras, explores their properties, links to trivial extensions of skew-gentle algebras, and characterizes those of finite representation type.

Findings

Skew-Brauer graph algebras are symmetric.

They generalize Brauer graph algebras with additional data.

Finite representation type skew-Brauer algebras are characterized.

Abstract

In this work, we introduce a new class of algebras called skew-Brauer graph algebras, which generalize the well-known Brauer graph algebras. We establish that skew-Brauer graph algebras are symmetric and can be defined using 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 multiplicity function identically equal to one, generalizing a result over gentle algebras. We also characterize skew-Brauer algebras of finite representation type. Finally, we provide a geometric interpretation of cut-sets and reflections of algebras using orbifold dissections.