Geometry of the moment map for representations of quivers. (English) Zbl 1037.16007

Crawley-Boevey, William

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.

MSC:

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

Keywords:

quiver representations; moment maps; preprojective algebras