Brauer Configuration Algebras Induced by Integer Partitions and Their Applications in the Theory of Branched Coverings

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 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.

Keywords

• branched covering
• Brauer configuration algebra (BCA)
• Hurwitz condition
• integer partition
• path algebra
• quiver representation