# Additive functions for quivers with relations

Colloquium Mathematicae (1999)

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

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topLenzing, 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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