Additive functions on quivers
type: Item
instance of: scholarly article
title: Additive functions on quivers
zbMATH Open document ID: 1015.05045
DOI: 10.1016/S0024-3795(02)00409-3
author: Helmut Lenzing
author: Liane Hasenberg
published in: Linear Algebra and its Applications
publication date: 2003-05-25T00:00:00Z
review text: An integral function on the set of vertices of a graph is additive if twice its value at any vertex \(v\) equals the sum of its values at all adjacent vertices, counting multiple edges, or equivalently, if the function is an eigenvector of a graph with eigenvalue 2. The authors study integral functions on finite quivers, i.e. finite oriented graphs without oriented cycles, relating the concept of additivity to the radical of the homological Euler form, and discuss the existence and constructions of their additive functions.
reviewed by: Dragan Stevanović
Mathematics Subject Classification ID: 05C50
zbMATH DE Number: 1915496
zbMATH Keywords: additive function
zbMATH Keywords: Euler form
zbMATH Keywords: quiver
zbMATH Keywords: graph
zbMATH Keywords: coxeter polynomial
zbMATH Keywords: Cartan matrix
MaRDI profile type: Publication
cites work: Sur les valeurs propres de la transformation de Coxeter
cites work: COXETER FUNCTORS AND GABRIEL'S THEOREM
cites work: Methods to determine Coxeter polynomials
cites work: Q4270323
cites work: Additive functions for quivers with relations
cites work: Q4311992
cites work: Q4224324
cites work: Tame algebras and integral quadratic forms
description: scientific article; zbMATH DE number 1915496