Geometry of the Moment Map for Representations of Quivers

Compositio Mathematica

Volumn 126, Issue 3, 2001, Pages 257-293

  Crawley Boevey, William ^a  

^a UNIVERSITY OF LEEDS   (United Kingdom)

Author keywords

Moment map; Preprojective algebra; Quiver representation

Indexed keywords

EID: 0000669075     PISSN: 0010437X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1017558904030     Document Type: Article

References (23)

1. Bergman, G. M. and Dicks, W.: Universal derivations and universal ring constructions, Pacific J. Math. 79 (1978), 293-337.
2. Cassens, H. and Slodowy, P.: On Kleinian singularities and quivers, Singularities (Oberwolfach, 1996), Birkhäuser, Basel, 1998, pp. 263-288.
3. Crawley-Boevey, W.: Preprojective algebras, differential operators and a Conze embedding for deformations of Kleinian singularities, Comment. Math. Helv. 74 (1999), 548-574.
4. Crawley-Boevey, W.: On the exceptional fibres of Kleinian singularities, Amer. J. Math. 122 (2000), 1027-1037.
5. Crawley-Boevey, W. and Holland, M. P.: Noncommutative deformations of Kleinian singularities, Duke Math. J. 92 (1998), 605-635.
6. Grothendieck, A. and Dieudonné, J.: Eléments de géométrie algébrique IV, part 2, Publ. Math. IHES 24 (1965).
7. Kac, V. G. : Infinite root systems, representations of graphs and invariant theory, Invent. Math. 56 (1980), 57-92.
8. Kac, V. G.: Root systems, representations of quivers and invariant theory, In: F. Gherardelli (ed.), Invariant Theory, Proc. Montecatini 1982, Lecture Notes in Math. 996, Springer, Berlin, 1983, pp. 74-108.
9. King, A. D.: Moduli of representations of finite dimensional algebras, Quart. J. Math. Oxford 45 (1994), 515-530.
10. Kraft, H. and Riedtmann, Ch.: Geometry of representations of quivers, In: P. Webb (ed.), Representations of Algebras, Proc. Durham 1985, London Math. Soc. Lecture Note Series 116, Cambridge Univ. Press, 1986, pp. 109-145.
11. Kronheimer, P. B.: The construction of ALE spaces as hyper-Kahler quotients, J. Differential Geom. 29 (1989), 665-683.
12. Le Bruyn, L. and Procesi, C.: Semisimple representations of quivers, Trans. Amer. Math. Soc. 317 (1990), 585-598.
13. Luna, D.: Slices étales, Bull. Soc. Math. France, Mémoire 33 (1973), 81-105.
14. Lusztig, G.: Quivers, perverse sheaves, and quantized enveloping algebras, J. Amer. Math. Soc. 4 (1991), 365-421.
15. Marsden, J. and Weinstein, A.: Reduction of symplectic manifolds with symmetry, Rep. Math. Phys. 5 (1974), 121-130.
16. Nakajima, H.: Instantons on ALE spaces, quiver varieties, and Kac-Moody algebras, Duke Math. J. 76 (1994), 365-416.
17. Nakajima, H.: Varieties associated with quivers, In: R. Bautista et al. (eds), Representation theory of algebras and related topics, Canadian Math. Soc. Conf. Proc. 19, Amer. Math. Soc., Providence, 1996.
18. Nakajima, H.: Quiver varieties and Kac-Moody algebras, Duke Math. J. 91 (1998), 515-560.
19. Nakajima, H.: Quiver varieties and finite dimensional representations of quantum affine algebras, J. Amer. Math. Soc. 14 (2001), 145-238.
20. Ringel, C. M.: Tame Algebras and Integral Quadratic Forms, Lecture Notes in Math. 1099, Springer, Berlin, 1984.
21. Rump, W.: Doubling a path algebra, or: how to extend indecomposable modules to simple modules, An. St. Ovidius Constantza 4 (1996), 174-185.
22. Schofield, A.: General representations of quivers, Proc. London Math. Soc. 65 (1992), 46-64.
23. Schofield, A.: Quivers and Kac-Moody Lie algebras, manuscript, 23pp.