On representations of algebras with radical square zero

TL;DR

This paper establishes a new correspondence between representations of algebras with radical square zero and species, enabling reconstruction of the Auslander-Reiten quiver of the algebra from that of the species.

Contribution

It introduces a novel embedding of the stable category of such algebra representations into the species' representation category and details how to reconstruct the Auslander-Reiten quiver.

Findings

Stable category of algebra representations embeds into species representations

Reconstruction of Auslander-Reiten quiver from species quiver

New correspondence simplifies analysis of radical square zero algebras

Abstract

We consider a new correspondence between representations of algebras with radical square zero and representations of species. We show that the stable category of representations of such algebra embeds into the representation category of the corresponding species and show how one reconstruct the Auslander-Reiten quiver of the algebra from the Auslander-Reiten quiver of the species.