Brauer Configuration Algebras and Matrix Problems to Categorify Integer Sequences

TL;DR

This paper uses Brauer configuration algebras and matrix problems to categorify integer sequences, linking algebraic invariants to classical problems like the Kronecker and four subspace problems.

Contribution

It introduces a novel approach connecting Brauer configuration algebras with categorification of integer sequences through invariants related to classical matrix problems.

Findings

Bijections between algebra invariants and matrix problem solutions

Dimensions of Brauer configuration algebras and centers are computed

Categorification of integer sequences achieved via algebraic invariants

Abstract

Bijections between invariants associated to indecomposable projective modules over some suitable Brauer configuration algebras and invariants associated to solutions of the Kronecker problem and the four subspace problem are used to categorify integer sequences in the sense of Ringel and Fahr. Dimensions of the Brauer configuration algebras and their corresponding centers involved in the different processes are given as well.