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

TL;DR

This paper classifies the Auslander-Reiten components of the bounded derived category for cluster-tilted algebras of type A, using combinatorial methods involving homotopy strings and bands.

Contribution

It provides a combinatorial classification of Auslander-Reiten components for a specific class of algebras, extending understanding of their derived categories.

Findings

Complete classification of Auslander-Reiten components for the given algebras.

Introduction of homotopy strings and bands as tools for analysis.

Enhanced understanding of the structure of the bounded derived category.

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.