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Stable representations of quivers. (English) Zbl 1040.16011
Summary: Let $$Q$$ be a finite quiver without oriented cycles and let $$kQ$$ be the path algebra of $$Q$$ over an algebraically closed field $$k$$. We investigate stable finite-dimensional representations of $$Q$$. That is for a fixed dimension vector $$d$$ and a fixed weight $$\theta$$ we consider $$\theta$$-stable representations of $$Q$$ with dimension vector $$d$$. If we wish to compare also representations with different dimension vectors, then it is more convenient to consider a slope $$\mu$$ instead of a weight $$\theta$$. In particular, we apply the results of Harder-Narasimhan on natural filtrations associated to any fixed slope $$\mu$$ to the category of representations of $$Q$$. Further we introduce the wall system for weights with respect to a fixed dimension vector $$d$$ and consider several examples.

##### MSC:
 16G20 Representations of quivers and partially ordered sets
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##### References:
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