Brauer Configuration Algebras Arising from Dyck Paths

Agustín Moreno Cañadas, Gabriel Bravo Rios and Isaías David Marín Gaviria
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Agustín Moreno Cañadas: Departamento de Matemáticas, Universidad Nacional de Colombia, Edificio Yu Takeuchi 404, Kra 30 No 45-03, Bogotá 11001000, Colombia
Gabriel Bravo Rios: Departamento de Matemáticas, Universidad Nacional de Colombia, Edificio Yu Takeuchi 404, Kra 30 No 45-03, Bogotá 11001000, Colombia
Isaías David Marín Gaviria: Departamento de Matemáticas, Universidad Nacional de Colombia, Edificio Yu Takeuchi 404, Kra 30 No 45-03, Bogotá 11001000, Colombia

Mathematics, 2022, vol. 10, issue 9, 1-15

Abstract: The enumeration of Dyck paths is one of the most remarkable problems in Catalan combinatorics. Recently introduced categories of Dyck paths have allowed interactions between the theory of representation of algebras and cluster algebras theory. As another application of Dyck paths theory, we present Brauer configurations, whose polygons are defined by these types of paths. It is also proved that dimensions of the induced Brauer configuration algebras and the corresponding centers are given via some integer sequences related to Catalan triangle entries.

Keywords: Brauer configuration algebra; Catalan triangle; Dyck path; path algebra (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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