Additive functions on trees

• Autorzy: Piroska Lakatos
• Języki publikacji: EN

Abstrakty

EN

The motivation for considering positive additive functions on trees was a characterization of extended Dynkin graphs (see I. Reiten [R]) and applications of additive functions in representation theory (see H. Lenzing and I. Reiten [LR] and T. Hübner [H]).
We consider graphs equipped with integer-valued functions, i.e. valued graphs (see also [DR]). Methods are given for constructing additive functions on valued trees (in particular on Euclidean graphs) and for characterizing their structure. We introduce the concept of almost additive functions, which are additive on each vertex of a graph except one (called the exceptional vertex). On (valued) trees (with fixed exceptional vertex) the almost additive functions are unique up to rational multiples. For valued trees a necessary and sufficient condition is given for the existence of positive almost additive functions.

Kategorie tematyczne

• 05C05: Trees
• 16G20: Representations of quivers and partially ordered sets
• 16G70: Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2001
• Tom: 89
• Numer: 1
• Strony: 135-145

Daty

wydano

2001

Twórcy

autor

Piroska Lakatos

• Institute of Mathematics and Informatics, University of Debrecen, P.O. Box 12, 4010 Debrecen, Hungary

Identyfikatory

DOI

10.4064/cm89-1-10