Download PDF - Constructing the directing components of an algebraAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Constructing the directing components of an algebra

Authors 1, 1

Affiliations

  1. Instituto de Matemáticas, UNAM, México 04510, DF México

Bibliography

  1. M. Auslander, I. Reiten and S. Smalο, Representation Theory of Artin Algebras, Cambridge Stud. Adv. Math. 36, Cambridge Univ. Press, 1995.
  2. R. Bautista, F. Larrión and L. Salmerón, On simply connected algebras, J. London Math. Soc. (2) 27 (2) (1983), 212-220.
  3. F. Coelho and D. Happel, Quasitilted algebras admit a preprojective component, to appear.
  4. P. Dräxler and J. A. de la Pe na, On the existence of postprojective components for algebras, Tsukuba J. Math. 20 (1996), 457-469.
  5. P. Gabriel, Auslander-Reiten sequences and representation-finite algebras, in: Representation Theory I (Proc. ICRA II, Ottawa, 1979), Lecture Notes in Math. 831, Springer, 1980, 1-71.
  6. P. Gabriel and J. A. de la Pe na, On algebras: wild and tame, in: Duration and Change. Fifty Years at Oberwolfach, Springer, 1994, 177-210.
  7. W. Geigle and H. Lenzing, Perpendicular categories with applications to representations and sheaves, J. Algebra 144 (1991), 273-343.
  8. D. Happel and C. M. Ringel, Directing projective modules, Arch. Math. (Basel) 60 (1993), 237-246.
  9. S. Kasjan and J. A. de la Pe na, Constructing the preprojective components of an algebra, J. Algebra 179 (1996), 793-807.
  10. O. Kerner, Tilting wild algebras, J. London Math. Soc. 39 (1989), 29-47.
  11. S. Liu, Tilted algebras and generalized standard Auslander-Reiten components, Arch. Math. (Basel) 61 (1993), 12-19.
  12. J. A. de la Pe na and M. Takane, Spectral properties of Coxeter transformations and applications, ibid. 55 (1990), 120-134.
  13. C. M. Ringel, Tame algebras, in: Representation Theory I (Proc. ICRA II, Ottawa, 1979), Lecture Notes in Math. 831, Springer, 1980, 137-287.
  14. C. M. Ringel, Tame Algebras and Integral Quadratic Forms, Lecture Notes in Math. 1099, Springer, Berlin, 1984.
  15. C. M. Ringel, The spectral radius of the Coxeter transformation for a generalized Cartan matrix, Math. Ann. 300 (1994), 331-339.
  16. A. Skowroński, Cycles in module categories, in: Finite Dimensional Algebras and Related Topics, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 424, Kluwer, 1994, 309-345.
  17. A. Skowroński, Generalized standard Auslander-Reiten components without oriented cycles, Osaka J. Math. 30 (1993), 515-527.
  18. A. Skowroński and S. Smalο, Directing modules, J. Algebra 147 (1992), 137-146.
  19. A. Skowroński and M. Wenderlich, Artin algebras with directing indecomposable projective modules, ibid. 165 (1994), 507-530.
  20. H. Strauß, On the perpendicular category of a partial tilting module, ibid. 144 (1991), 43-66.
Colloquium Mathematicum
1997/74/1
Export to PBN, Opens in new tab
Pages:
29-46
Main language of publication
English
Received
1996-04-01
Accepted
1996-10-16
Published
1997
Exact and natural sciences