Additive functions for quivers with relations

Volume 82 / 1999

Helmut Lenzing, Idun Reiten Colloquium Mathematicum 82 (1999), 85-103 DOI: 10.4064/cm-82-1-85-103


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.


  • Helmut Lenzing
  • Idun Reiten

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