Almost $\cal D$-split sequences and derived equivalences

Wei Hu, Changchang Xi

Published 2008-10-27Version 1

In this paper, we introduce almost $\cal D$-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.