Auslander-Reiten sequences and $t$-structures on the homotopy category of an abelian category

TL;DR

This paper employs t-structures and Watts' theorem on the homotopy category of an artin algebra to establish the existence of Auslander-Reiten sequences for modules over R.

Contribution

It provides a new proof for the existence of Auslander-Reiten sequences using t-structures and Watts' representability theorem.

Findings

Existence of Auslander-Reiten sequences proven for R-modules

Application of t-structures in homotopy categories

Use of Watts' theorem in representation theory

Abstract

We use $t$-structures on the homotopy category $K^b(R-mod)$ for an artin algebra $R$ and Watts' representability theorem to give an existence proof for Auslander-Reiten sequences of $R$-modules.