# On additive functions for stable translation quivers

Colloquium Mathematicae (1999)

- Volume: 79, Issue: 2, page 203-210
- ISSN: 0010-1354

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topBobiński, Grzegorz. "On additive functions for stable translation quivers." Colloquium Mathematicae 79.2 (1999): 203-210. <http://eudml.org/doc/210635>.

@article{Bobiński1999,

abstract = {The aim of this note is to give a complete description of the positive additive functions for the stable nonperiodic translation quivers with finitely many orbits. In particular, we show that all positive additive functions on the stable translation quivers of Euclidean type (respectively, of wild type) are periodic, and hence bounded (respectively, are unbounded, and hence nonperiodic).},

author = {Bobiński, Grzegorz},

journal = {Colloquium Mathematicae},

keywords = {additive functions; representations of quivers; dimension vectors; regular representations; Coxeter matrices; Dynkin diagrams; Euclidean diagrams},

language = {eng},

number = {2},

pages = {203-210},

title = {On additive functions for stable translation quivers},

url = {http://eudml.org/doc/210635},

volume = {79},

year = {1999},

}

TY - JOUR

AU - Bobiński, Grzegorz

TI - On additive functions for stable translation quivers

JO - Colloquium Mathematicae

PY - 1999

VL - 79

IS - 2

SP - 203

EP - 210

AB - The aim of this note is to give a complete description of the positive additive functions for the stable nonperiodic translation quivers with finitely many orbits. In particular, we show that all positive additive functions on the stable translation quivers of Euclidean type (respectively, of wild type) are periodic, and hence bounded (respectively, are unbounded, and hence nonperiodic).

LA - eng

KW - additive functions; representations of quivers; dimension vectors; regular representations; Coxeter matrices; Dynkin diagrams; Euclidean diagrams

UR - http://eudml.org/doc/210635

ER -

## References

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- [6] C. M. Ringel, Finite dimensional hereditary algebras of wild representation type, Math. Z. 161 (1978), 235-255. Zbl0415.16023
- [7] C. M. Ringel, Tame Algebras and Integral Quadratic Forms, Lecture Notes in Math. 1099, Springer, 1984.
- [8] Y. Zhang, The modules in any component of the AR-quiver of a wild hereditary artin algebra are uniquely determined by their composition factors, Arch. Math. (Basel) 53 (1989), 250-251 Zbl0651.16013

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