The Auslander-Reiten components of the bounded derived category for a cluster-tilted algebra of type \~A

Abstract

We classify the Auslander-Reiten components of the bounded derived category of \Lambda, where {\Lambda} is a cluster-tilted of type \~A. The main tool is the combinatoric description of the indecomposable complexes in the bounded homotopy category via homotopy strings and homotopy bands.