On degenerations and extensions of finite dimensional modules

Advances in Mathematics

Volumn 121, Issue 2, 1996, Pages 245-287

  Bongartz, Klaus ^a  

^a UNIVERSITY OF WUPPERTAL   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030578647     PISSN: 00018708     EISSN: None     Source Type: Journal    
DOI: 10.1006/aima.1996.0053     Document Type: Article

References (40)

1. m, J. Algebra 93 (1985), 376-412.
2. m, Adv. Math. 52 (1984), 81-172.
3. M. Artin, On Azumaya algebras and finite dimensional representations of rings, J. Algebra 11 (1969), 532-563.
4. M. Auslander and I. Reiten, Modules determined by their composition factors, Illinois J. Math. 29 (1985), 289-301.
5. M. Auslander and S. O. Smalo, Preprojective modules over artin algebras, J. Algebra 66 (1980), 61-122.
6. M. Auslander and S. O. Smalo, Almost split sequences in subcategories, J. Algebra 69 (1981), 426-455.
7. R. Bautista, P. Gabriel, A. V. Roiter, and L. Salmeron, Representation finite algebras and multiplicity bases, Invent. Math. 81 (1985), 217-285.
8. K. Bongartz, On omnipresent modules in preprojective components, Comm. Algebra 11, No. 18 (1983), 2125-2128.
9. K. Bongartz, Indecomposables over representation-finite algebras are extensions of an indecomposable and a simple, Math. Z. 187 (1984), 75-80.
10. K. Bongartz, "Quadratic Forms and Finite Representation Type," Springer Lecture Notes in Math, Vol. 1146, pp. 325-339, Springer-Verlag, 1986.
11. K. Bongartz, Critical simply connected algebra, Manuscripta Math. 46 (1984), 117-136.
12. K. Bongartz, Gauss-Elimination und der grösste gemeinsame direkte Summand von zwei endlichdimensionalen Moduln, Arch. Math. 53 (1989), 256-258.
13. K. Bongartz, Schichten von Matrizen sind rationale Varietäten, Math. Ann. 283 (1989), 53-64.
14. K. Bongartz, A geometric version of the Morita equivalence, J. Algebra, to appear; preprint, 16pp., 1989.
15. K. Bongartz and C. Riedtmann, Algèbres stablement héréditaires, C.R. Acad. Sci. Paris Sér. A, B 288 (1979), 703-706.
16. W. Borho and H. P. Kraft, Ueber Bahnen und deren Deformationen bei linearen Aktionen reduktiver Gruppen, Comment. Math. Helv. 54 (1979), 61-104.
17. D. Flanigan, Deformations of algebra modules, J. Algebra 31 (1974), 245-256.
18. P. Gabriel, Unzerlegbare Darstellungen, I, Manuscripta Math. 6 (1972), 71-103.
19. P. Gabriel, "Finite Representation Type is Open," Springer Lecture Notes, Vol. 488, pp. 132-155, Springer-Verlag, 1975.
20. P. Gabriel, "Auslander-Reiten Sequences and Representation Finite Algebras," Springer Lecture Notes, Vol. 831, pp. 1-71, Springer-Verlag, New York/Berlin, 1979.
21. F. R. Gantmacher, "The Theory of Matrices," Vols. I and II, Chelsea, New York, 1960.
22. M. Gerstenhaber, On nilalgebras and linear varieties of nilpotent matrices, III, Ann. of Math. 70 (1959), 167-205.
23. F. Grunewald and J. O'Halloran, A characterization of orbit closure and applications, J. Algebra 116 (1988), 163-175.
24. D. Happel and C. M. Ringel, Tilted algebras, Trans. Amer. Math. Soc. 274 (1982), 339-443.
25. W. Hesselink, Singularities in the nilpotent scheme of a classical group, Trans. Amer. Math. Soc. 222 (1976), 1-32.
26. B. Kagstrom and A. Ruhe, "Matrix Pencils," Springer Lecture Notes in Math., Vol. 973, Springer-Verlag, New York/Berlin.
27. H. P. Kraft, "Geometrische Methoden in der Invariantentheorie," Vieweg Verlag, 1984.
28. H. P. Kraft and C. Riedtmann, "Geometry of Representations of Quivers," Lecture Notes in Math., Vol. 116, pp. 109-147, Springer-Verlag, New York/Berlin, 1985.
29. U. Markolf, "Entartungen von Darstellungen zu Dynkin-Köchern," thesis, University of Wuppertal.
30. D. Mumford and J. Fogarty, "Geometric Invariant Theory," Ergebnisse Band 34, Springer-Verlag, Berlin/New York, 1982.
31. P. E. Newstead, "Introduction to Moduli Problems and Orbit Spaces," Tata Institute, Bombay, 1978.
32. C. Riedtmann, Generations for representations of quivers with relations, Ann. Sci. Ecole Norm. Sup. (4) 19 (1986), 275-301.
33. C. Riedtmann and A. Schofield, On open orbits and their complements, preprint, 24 pp., 1988.
34. C. M. Ringel, The rational invariants of tame quivers, Invent. Math. 58 (1980), 217-239.
35. C. M. Ringel, "Tame Algebras and Quadratic Forms," Springer Lecture Notes in Math., Vol. 1099, Springer-Verlag, New York/Berlin, 1984.
36. A. H. Schofield, Bounding the global dimension in terms of the dimension, Bull. London Math. Soc. 17 (1985), 393-394.
37. P. Slodowy, "Simple Singularities and Simple Algebraic Groups," Springer Lecture Notes in Math., Vol. 815, Springer-Verlag, New York/Berlin, 1980.
38. R. Steinberg, "Conjugacy Classes in Algebraic Groups," Springer Lecture Notes in Math., Vol. 366, Springer-Verlag, New York/Berlin, 1974.
39. D. Voigt, "Endliche algebraische Gruppen," Springer Lecture Notes in Math., Vol. 592, Springer-Verlag, New York/Berlin, 1977.
40. P. Gabriel, "The Universal Cover of a Representation-Finite Algebra," Springer Lecture Notes in Math., Vol. 903, pp. 68-105, Springer-Verlag, New York/Berlin, 1981.