2024/10/02 by Ana García Elsener, Elsener, Ana García, Victoria Guazzelli +3
Mathematics · #05E10 #16G20 #16S35 #16S70 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2410.01942
openalex publication_date 2024/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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.