The Cartan Matrix of a Brauer Configuration Algebra

TL;DR

This paper demonstrates how to compute the Cartan matrix entries of a Brauer configuration algebra using its combinatorial data, providing a method to analyze these algebraic structures.

Contribution

It introduces a combinatorial approach to determine the Cartan matrix of Brauer configuration algebras, which was not previously explicit.

Findings

Method for computing Cartan matrix entries from combinatorial data

Explicit formulas linking configuration structure to algebra properties

Enhanced understanding of algebraic invariants in Brauer configurations

Abstract

Using the combinatorial information of a Brauer configuration is possible to compute each entry of the Cartan matrix of the algebra associated to the Brauer configuration.