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Keywords = Brauer configuration algebra (BCA)

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21 pages, 543 KiB  
Article
Brauer Configuration Algebras Induced by Integer Partitions and Their Applications in the Theory of Branched Coverings
by Agustín Moreno Cañadas, José Gregorio Rodríguez-Nieto and Olga Patricia Salazar Díaz
Mathematics 2024, 12(22), 3626; https://doi.org/10.3390/math12223626 - 20 Nov 2024
Cited by 1 | Viewed by 1032
Abstract
Brauer configuration algebras are path algebras induced by appropriated multiset systems. Since their structures underlie combinatorial data, the general description of some of their algebraic invariants (e.g., their dimensions or the dimensions of their centers) is a hard problem. Integer partitions and compositions [...] Read more.
Brauer configuration algebras are path algebras induced by appropriated multiset systems. Since their structures underlie combinatorial data, the general description of some of their algebraic invariants (e.g., their dimensions or the dimensions of their centers) is a hard problem. Integer partitions and compositions of a given integer number are examples of multiset systems which can be used to define Brauer configuration algebras. This paper gives formulas for the dimensions of Brauer configuration algebras (and their centers) induced by some integer partitions. As an application of these results, we give examples of Brauer configurations, which can be realized as branch data of suitable branched coverings over different surfaces. Full article
(This article belongs to the Special Issue Algebra and Discrete Mathematics, 4th Edition)
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