A generalization of the nilpotency index of the radical of the module category of an algebra

TL;DR

This paper generalizes the calculation of the nilpotency index of the radical of the module category for certain finite-dimensional algebras, extending previous results to broader classes such as monomial and toupie algebras.

Contribution

It identifies minimal vertices needed to compute the nilpotency index for these algebras without the restriction of length components in the Auslander-Reiten quiver.

Findings

Determined vertices sufficient for nilpotency index calculation

Extended results to monomial and toupie algebras

Generalized previous nilpotency index formulas

Abstract

Let $A$ be a finite dimensional representation-finite algebra over an algebraically closed field. The aim of this work is to generalize the results proven in CGS. Precisely, we determine which vertices of $Q_A$ are sufficient to be considered in order to compute the nilpotency index of the radical of the module category of a monomial algebra and a toupie algebra $A$, when the Auslander-Reiten quiver is not necessarily a component with length.