Trivial extensions of monomial algebras are symmetric fractional Brauer configuration algebras

TL;DR

This paper introduces a new combinatorial framework linking monomial algebras to symmetric fractional Brauer configuration algebras, showing they are trivial extensions and establishing a classification correspondence.

Contribution

It provides equivalent definitions for fractional Brauer configuration algebras and demonstrates a bijective correspondence with monomial algebras via combinatorial data.

Findings

Fractional Brauer configuration algebras are isomorphic to trivial extensions of monomial algebras.

A one-to-one correspondence exists between monomial algebras and certain symmetric fractional Brauer configuration algebras.

The paper characterizes the classification of monomial algebras through combinatorial configurations.

Abstract

By providing equivalent definitions of fractional Brauer configuration algebras in certain special cases, we associate to each monomial algebra some combinatorial data called a fractional Brauer configuration, from which we construct a corresponding fractional Brauer configuration algebra. We show that this algebra is isomorphic to the trivial extension of the given monomial algebra. Furthermore, we establish a one-to-one correspondence between the isomorphism classes of monomial algebras and the equivalence classes of pairs consisting of a symmetric fractional Brauer configuration algebra of type S with a free fractional-degree function and an admissible cut on it.