Additive functions for quivers with relations extend the classical concept of additive functions for graphs. It is shown that the concept, recently introduced by T. Hübner in a special context, can be defined for different homological levels. The existence of such functions for level 2 resp. ∞ relates to a nonzero radical of the Tits resp. Euler form. We derive the existence of nonnegative additive functions from a family of stable tubes which stay tubes in the derived category, we investigate when this situation does appear and we study the restrictions imposed by the existence of a positive additive function.
@article{bwmeta1.element.bwnjournal-article-cmv82i1p85bwm,
author = {Helmut Lenzing and Idun Reiten},
title = {Additive functions for quivers with relations},
journal = {Colloquium Mathematicae},
volume = {79},
year = {1999},
pages = {85-103},
zbl = {0984.16015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv82i1p85bwm}
}
Lenzing, Helmut; Reiten, Idun. Additive functions for quivers with relations. Colloquium Mathematicae, Tome 79 (1999) pp. 85-103. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv82i1p85bwm/
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