Almost $\mathcal{D}$-split sequences and derived equivalences

Abstract

In this paper, we introduce almost $\mathcal{D}$-split sequences and establish an elementary but somewhat surprising connection between derived equivalences and Auslander-Reiten sequences via BB-tilting modules. In particular, we obtain derived equivalences from Auslander-Reiten sequences (or $n$-almost split sequences), and Auslander-Reiten triangles.