2009/06/26 by Scherotzke, Sarah
#FOS: Mathematics #K-Theory and Homology (math.KT) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.0906.4987
We deduce a necessary condition for Auslander-Reiten components of the bounded derived category of a finite dimensional algebra to have Euclidean tree class by classifying certain types of irreducible maps in the category of complexes. This result shows that there are only finitely many Auslander-Reiten components with Euclidean tree class up to shift. Also the Auslander-Reiten quiver of certain classes of Nakayama are computed directly and it is shown that they are piecewise hereditary. Finally we state a condition for \Z[A∞]-components to appear in the Auslander-Reiten quiver generalizing a result in \citeW.