Homotopy categories of injective modules over derived discrete algebras

TL;DR

This paper classifies indecomposable objects in the homotopy category of injective modules over derived discrete algebras, revealing that all such objects are endofinite, with a focus on radical square zero self-injective algebras.

Contribution

It provides a complete classification of indecomposable objects in the homotopy category for a class of derived discrete algebras, highlighting their endofinite nature.

Findings

All indecomposable objects are endofinite.

Classification achieved for radical square zero self-injective algebras.

Homotopy category structure elucidated for derived discrete algebras.

Abstract

We study the homotopy category $ K(\Inj A)$ of all injective modules over a finite dimensional algebra $A$ with discrete derived category. We give a classification of the indecomposable objects of $ K(\Inj A)$ for any radical square zero self-injective algebra $A$. In particular, every indecomposable object is endofinite.