Crawley-Boevey, William Geometry of the moment map for representations of quivers. (English) Zbl 1037.16007 Compos. Math. 126, No. 3, 257-293 (2001). 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. Cited in 4 ReviewsCited in 85 Documents MSC: 16G20 Representations of quivers and partially ordered sets 53D20 Momentum maps; symplectic reduction Keywords:quiver representations; moment maps; preprojective algebras PDF BibTeX XML Cite \textit{W. Crawley-Boevey}, Compos. Math. 126, No. 3, 257--293 (2001; Zbl 1037.16007) Full Text: DOI