Additive functions for quivers with relations

Helmut Lenzing; Idun Reiten

Colloquium Mathematicae (1999)

  • Volume: 82, Issue: 1, page 85-103
  • ISSN: 0010-1354

Abstract

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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.

How to cite

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Lenzing, Helmut, and Reiten, Idun. "Additive functions for quivers with relations." Colloquium Mathematicae 82.1 (1999): 85-103. <http://eudml.org/doc/210753>.

@article{Lenzing1999,
abstract = {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.},
author = {Lenzing, Helmut, Reiten, Idun},
journal = {Colloquium Mathematicae},
keywords = {quivers; Euler forms; additive functions; stable tubes; derived categories; Tits forms},
language = {eng},
number = {1},
pages = {85-103},
title = {Additive functions for quivers with relations},
url = {http://eudml.org/doc/210753},
volume = {82},
year = {1999},
}

TY - JOUR
AU - Lenzing, Helmut
AU - Reiten, Idun
TI - Additive functions for quivers with relations
JO - Colloquium Mathematicae
PY - 1999
VL - 82
IS - 1
SP - 85
EP - 103
AB - 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.
LA - eng
KW - quivers; Euler forms; additive functions; stable tubes; derived categories; Tits forms
UR - http://eudml.org/doc/210753
ER -

References

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