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Geometry of the Moment Map for Representations of Quivers
Authors:William Crawley-Boevey
Institution:(1) Department of Pure Mathematics, University of Leeds, Leeds, LS2 9JT, U.K.
Abstract: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.
Keywords:quiver representation  moment map  preprojective algebra
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