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Stable representations of quivers

By Lutz Hille and José Antonio de la Peña


AbstractLet Q be a finite quiver without oriented cycles and let kQ 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 θ we consider θ-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 μ instead of a weight θ. In particular, we apply the results of Harder–Narasimhan on natural filtrations associated to any fixed slope μ 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

Publisher: Published by Elsevier B.V.
Year: 2002
DOI identifier: 10.1016/S0022-4049(01)00167-0
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