The Dimension of the Center of a Brauer Configuration Algebra

TL;DR

This paper calculates the dimension of the center of Brauer configuration algebras by explicitly determining a basis, providing insight into their algebraic structure.

Contribution

It introduces a method to compute the center's dimension for any Brauer configuration algebra by constructing a specific basis.

Findings

Explicit basis for the center of Brauer configuration algebras

Dimension formula for the center based on the basis

Applicable to all Brauer configuration algebras

Abstract

We consider an arbitrary algebra of the class of Brauer configuration algebras and calculate the dimension of the center by determining a $K$-basis.