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Geometry of the moment map for representations of quivers. (English) Zbl 1037.16007
Summary: We study the moment map associated to the cotangent bundle of the space of representations of a quiver, determining when it is flat, and giving a stratification of its Marsden-Weinstein reductions. In order to do this we determine the possible dimension vectors of simple representations of deformed preprojective algebras. In an appendix we use deformed preprojective algebras to give a simple proof of much of Kac’s Theorem on representations of quivers in characteristic zero.

MSC:
16G20 Representations of quivers and partially ordered sets
53D20 Momentum maps; symplectic reduction
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