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Stable representations of quivers

✍ Scribed by Lutz Hille; José Antonio de la Peña

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
181 KB
Volume
172
Category
Article
ISSN
0022-4049

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✦ Synopsis

Let Q be a ÿnite quiver without oriented cycles and let kQ the path algebra of Q over an algebraically closed ÿeld k. We investigate stable ÿnite dimensional representations of Q. That is for a ÿxed dimension vector d and a ÿxed weight  we consider Â-stable representations of Q with dimension vector d. If we wish to compare also representations with di erent dimension vectors, then it is more convenient to consider a slope instead of a weight Â. In particular, we apply the results of Harder-Narasimhan on natural ÿltrations associated to any ÿxed slope to the category of representations of Q. Further we introduce the wall system for weights with respect to a ÿxed dimension vector d and consider several examples.

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