Tilting in Abelian categories and quasitilted algebras

Memoirs of the American Mathematical Society

Volumn , Issue 575, 1996, Pages 1-87

  Happel, Dieter ^a   Reiten, Idun ^a   Smalø, Sverre O ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030100229     PISSN: 00659266     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (58)

1. [An] H. H. Andersen, Tensor products of quantized tilting modules, Preprint Aarhus Univ.
2. [AGR] M. Auslander, E. Green and I. Reiten, Modules with waists Ill. J. Math., 19,no. 3 (1975) 467-478.
3. [APR] M. Auslander, M. I. Platzeck and I. Reiten, Coxeter functors without diagrams, Trans. Amer. Math. Soc 250 (1979) 1-12.
4. [AR1] M. Auslander and I. Reiten, Representation theory of artin algebras III. Comm. in Algebra 3 (1975) 239-294.
5. [AR2] M. Auslander and I. Reiten, Modules determined by their composition factors, Ill.J. of Math 29 (1985) 280-301.
6. [AR3] M. Auslander and I. Reiten, Applications of Contravariantly finite Subcategories, Adv. in Math., Vol.86, No 1 (1991), 111-152.
7. [ARS] M. Auslander, I. Reiten and S. O. Smalø, Representation theory of artin algebras, Cambridge Univ. Press. 1995.
8. [As] I. Assem, Tilting theory - an introduction, Topics in Algebra, Banach Center Publications, Vol. 26 PWN, Warsaw (1990) 127-180.
9. [AS1] M. Auslander and S. O. Smalø, Preprojective modules over artin algebras, J. Algebra 66 (1980) 61-122.
10. [AS2] M. Auslander and S. O. Smalø, Almost split sequences in subcategories, J. Algebra 69 (1981), 426-454; Addendum J. Algebra 71 (1981), 592-594.
11. [AS2] M. Auslander and S. O. Smalø, Almost split sequences in subcategories, J. Algebra 69 (1981), 426-454; Addendum J. Algebra 71 (1981), 592-594.
12. [Ba] D Baer, Wild hereditary artin algebras and linear methods, Manuscr. Math. 55 (1986), 69-82.
13. [BB] S. Brenner and M. C. R. Butler, Generalizations of the Bernstein-Gelfand-Ponomarev reflection functors, Proc. Ottawa Conf. on Repr. theory 1989, Lecture Notes in Math. 832, 103-169, Springer-Verlag, Berlin-Heidelberg-New York (1980).
14. [BBD] A. A. Beilinson, J. Bernstein and P. Deligne Faisceaux pervers, Astérisque no 100 (1982)
15. n and problems of linear algebra, Funk. Anal. Priloz. 12 (1978), 69-69, English translation: Funct. Analysis Appl. 12 (1979) 214-216.
16. n and problems of linear algebra, Funk. Anal. Priloz. 12 (1978), 69-69, English translation: Funct. Analysis Appl. 12 (1979) 214-216.
17. n and problems of linear algebra. Funct.\ Anal\. appl\. 12 (1978), 212-214.
18. [BGP] I. Bernstein, I. M. Gelfand and V. A. Ponomarev, Coxeter functors and Gabriel's theorem, Usp. Mat. Nauk 28 (1973) 19-33 (English trans. Russ. Math. Surveys 28 (1973) 17-32.
19. [BGP] I. Bernstein, I. M. Gelfand and V. A. Ponomarev, Coxeter functors and Gabriel's theorem, Usp. Mat. Nauk 28 (1973) 19-33 (English trans. Russ. Math. Surveys 28 (1973) 17-32.
20. [Bo1] K. Bongartz, Critical simply connected algebras, Manuscr. Math. 46 (1984) 117-136.
21. [Bo2] K. Bongartz, Tilted algebras, Proc. of Conference on Representations of algebras, Puebla 1980, Lecture Notes in Math. 903, 26-38 Springer-Verlag, Berlin-Heidelberg-New York (1981).
22. [BS] R. Bautista and S. O. Smalø, Nonexistent cycles, Comm.in Algebra 11 (1983) 1755-1767.
23. [CPS] E. Cline, B. Parshall and L. Scott, Derived categories and Morita equivalence, J. Alg. 104 (1986) 397-409.
24. [Di] S. E. Dickson, A torsion theory for abelian categories, Trans. Amer. Math. Soc. 121 (1966) 223-235.
25. [Do] S. Donkin, On tilting modules for algebraic groups, Math. Zeitschr. (1) 212 (1993) 39-60.
26. [DR] V. Dlab and C. M. Ringel, Indecomposable representations of graphs and algebras, Memoirs Amer. Math. Soc. 173 (1976).
27. [FGR] R. M. Fossum, P. A. Griffith and I. Reiten, Trivial extensions of abelian categories, Lecture Notes in Math. 405, Springer-Verlag, Berlin-Heidelberg-New York (1975).
28. [GL] W. Geigle and H. Lenzing, Perpendicular categories with applications to representations and sheaves, J. Algebra 144 (1991), 273-343.
29. [Gr] P. P. Grivel, Categories derivees et fonteur derives, in Algebraic D-modules, Perspectives in Mathematics, vol. 2, Academic Press 1987.
30. [Hap1] D. Happel, On the derived category of a finite dimensional algebra, Comment. Math. Helvetica 62 (1987), 339-389.
31. [Hap2] D. Happel, Triangulated Categories in the Representation Theory of Finite Dimensional Algebras, London Math. Soc. Lecture Note Series, 119, (1988).
32. [Hap3] D. Happel, Auslander-Reiten triangles in derived categories of finite dimensional algebras, Proc. Amer. Math. Soc. 122 (1991), 641-648.
33. [Har1] R. Hartshorne, Residues and duality, Lecture Notes in Math. 20, Springer-Verlag, Berlin-Heidelberg-New York (1966).
34. [Har2] R. Hartshorne, Algebraic Geometry, Springer-verlag, Heidelberg 1977.
35. [Ho] M. Hoshino, Tilting modules and tosion theories, Bull. London Math. Soc. 14 (1982), 334-336.
36. [HR1] D. Happel and C. M. Ringel, Tilted algebras, Trans. Amer. Math. Soc., 274 (1982), 399-443.
37. [HR2] D. Happel and C. M. Ringel, Construction of Tilted algebras, Lecture Notes in Math. 903, 125-144, Springer-Verlag, Berlin-Heidelberg-New York (1981).
38. [HRS1] D. Happel, I. Reiten and S. O. Smalø, Quasitilted algebras, NATO Advanced Sci. Inst. Ser. C, Math, and Phys. Sci. vol 424 (1994) 163-182, Klüwer Academic Publishers.
39. D. Happel, I. Reiten and S. O. Smalø, Short cycles and sincere modules, Canadian Math. Soc. Conference Proceedings 14, (1993) 233-237.
40. D. Happel and D. Vossieck, Minimal algebras of infinite representation type with preprojective component, Manuscr. Math. 42 (1983), 221-243.
41. M. M. Kapranov, On the derived categories of coherent sheaves on some homogeneous spaces, Inv. Math. 92 (1988), 479-508.
42. O. Kerner, Preprojective components of wild tilted algebras, Manuscr. Math. 61 (1988), 429-445.
43. O. Kerner, Elementary Stones, Comm. Alg. 22, (1994) 1797-1806.
44. O. Kerner and F. Lukas, Elementary modules, To apear in Math. Z.
45. H. Lenzing and H. Meltzer, Tilting sheaves and concealed canonical algebras, in preparation.
46. H. Lenzing and J. A. de la Peña, Wild canonical algebras, preprint.
47. I. Palmer and J. E. Roos, Formules explicites pour la dimension homologique des anneux de matrices généralixées, Comptes rendus, s. A, 273 (1971), 1026-1029.
48. J. Rickard, Morita theory for Derived Categories, Journal of the London Math. Soc., 39, (1989), 436-456.
49. C. M. Ringel, Tame Algebras and Integral Quadratic Forms, Lecture Notes in Math. 1099, Springer-Verlag, Berlin-Heidelberg-New York (1984).
50. C.M. Ringel, Representation theory of finite-dimensional algebras, Proc. of Durham Symp. 1985, London Math. Soc. Lecture Note Series 116 (1986) 7-80.
51. C. M. Ringel, The canonical algebras, Topics in Algebra, Banach Center Publications, Vol. 26, Part 1, Warsaw (1990), 407-432.
52. C. M. Ringel, The category of modules with good filtration over a quasi-hereditary algebra has almost split sequences, Math. Z.
53. I. Reiten and C. Riedtmann, Skew group algebras in the representation theory of artin algebras, J. of Algebra 92 (1985), 224-282.
54. I. Reiten, A. Skowroński and S. O. Smalø, Short chains and short cycles of modules, Proc. Amer. Math. Soc., Vol. 117, No.2 (1993), 343-354.
55. A. N. Rudakov et. al., Helices and Vector Bundles. Seminaire Rudakov. London Math. Soc. LMS 148 (1990).
56. A. Skowroński, The regular Auslander-Reiten components containing directing modules, Proc. Amer. Math. Soc.
57. S. O. Smalø, Torsion theories and tilting modules, Bull. London Math. Soc. 16 (1984), 518-522.
58. J. L. Verdier, Catégories dérivée, état 0, SGA 4 1/2, Lecture Notes in Math. 569, 262-311 Springer-Verlag, Berlin-Heidelberg-New York (1977).