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arXiv · 2410.01942

Skew-Brauer graph algebras

Ana García Elsener·Victoria Guazzelli·Yadira Valdivieso
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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.

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Ana García Elsener, Victoria Guazzelli, Yadira Valdivieso. 2024-10-02. Skew-Brauer graph algebras. https://arxiv.org/abs/2410.01942

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