Skew-Brauer graph algebras
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.
Cite
@article{arxiv.2410.01942,
title = {Skew-Brauer graph algebras},
author = {Ana García Elsener and Victoria Guazzelli and Yadira Valdivieso},
journal= {arXiv preprint arXiv:2410.01942},
year = {2025}
}
Comments
Some changes in exposition. All figures are updated