Author: Kos Diveris
email: diveris@stolaf.edu
Address:
Department of Mathematics, St. Olaf College, Northfield, MN 55057, USA

Author: Marju Purin
email: purin@stolaf.edu
Address:
Department of Mathematics, St. Olaf College, Northfield, MN 55057, USA

Author: Peter Webb
email: webb@math.umn.edu
Address:
School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA

Title: Combinatorial restrictions on the tree class of the Auslander-Reiten quiver of a triangulated category

Abstract:
We show that if a connected, Hom-finite, Krull-Schmidt triangulated category 
has an Auslander-Reiten quiver component with Dynkin tree class then the 
category has Auslander-Reiten triangles and that component is the entire quiver.
This is an analogue for triangulated categories of a theorem of Auslander, 
and extends a previous result of Scherotzke. We also show that if there is a 
quiver component with extended Dynkin tree class, then other components  must 
also have extended Dynkin class or one of a small set of infinite trees, 
provided there is a non-zero homomorphism between the components. The proofs 
use the theory of additive functions.