On monomial algebras having the double centraliser property

TL;DR

This paper characterizes when finite dimensional algebras with the double centraliser property are monomial algebras, showing they are precisely Nakayama algebras defined by quiver and relations.

Contribution

It provides a complete characterization of monomial algebras with the double centraliser property as Nakayama algebras via quiver and relations.

Findings

A finite dimensional algebra with the double centraliser property is monomial if and only if it is a Nakayama algebra.

Such algebras are described explicitly by their quiver and relations.

The result links the double centraliser property to the structure of Nakayama algebras.

Abstract

Let $A$ be a finite dimensional algebra having the double centraliser property with respect to a minimal faithful projective-injective left module $Af$ for some idempotent $f$. We prove that in this case $A$ is a monomial algebra if and only if $A$ is a Nakayama algebra given by quiver and relations.