Mathematische Zeitschrift

, Volume 208, Issue 1, pp 209–223 | Cite as

The category of modules with good filtrations over a quasi-hereditary algebra has almost split sequences

  • Claus Michael Ringel
Article

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [AR] Auslander, M. Reiten, I.: Applications of contravariantly finite subcategories. Adv. Math. (to appear)Google Scholar
  2. [AS] Auslander, M., Smalø, S.: Almost split sequences in subcategories. J. Algebra69, 426–454 (1981)MATHCrossRefMathSciNetGoogle Scholar
  3. [CI] Collingwood, D.H., Irving, R.: A decomposition theorem for certain self-dual modules in the category O. Duke Math. J.58, 89–102 (1989)MATHCrossRefMathSciNetGoogle Scholar
  4. [CPS1] Cline, E., Parshall, B., Scott, L.: Finite dimensional algebras and highest weight categories, J. Reine Angew. Math.391, 85–99 (1988)MATHMathSciNetGoogle Scholar
  5. [CPS2] Cline, E., Parshall, B., Scott, L.: Duality in highest weight categories. (to appear)Google Scholar
  6. [DR1] Dlab, V., Ringel, C.M.: Quasi-hereditary algebras. Ill. J. Math.33, 280–291 (1989)MATHMathSciNetGoogle Scholar
  7. [DR2] Dlab, V., Ringel, C.M.: A construction for quasi-hereditary algebras. Compos. Math.70, 155–175 (1989)MATHMathSciNetGoogle Scholar
  8. [DR3] Dlab, V., Ringel, C.M.: Filtrations of right ideals related to projectivity of left ideals. In: Malliavin, M.-P. (ed.) Séminaire d'Algèbre. (Lect. Notes Math., vol. 1404, pp. 95–107, Berlin Heidelberg New York: Springer 1989Google Scholar
  9. [H] Happel, D.: Triangulated categories in the representation theory of finite dimensional algebras. (Lond. Math. Soc. Lect. Note Ser., vol. 119) Cambridge: Cambridge University Press 1988MATHGoogle Scholar
  10. [M] Miyashita, Y.: Tilting modules of finite projective dimension. Math. Z.193, 113–146 (1986)MATHCrossRefMathSciNetGoogle Scholar
  11. [PS] Parshall, B., Scott, L.: Derived categories, quasi-hereditary algebras and algebraic groups. Proceedings of the Ottawa-Moosonee Workshop in Algebra. Carleton Univ. Notes3 (1988)Google Scholar
  12. [R] Ringel, C.M.: Tame algebras and integral quadratic forms. (Lect. Notes Math., vol. 1099) Berlin Heidelberg New York: Springer 1984MATHGoogle Scholar
  13. [S] Scott, L.L.: Simulating algebraic geometry with algebra I: Derived categories and Morita theory, Proc. Symp. Pure Math.47.1, 271–282 (1987)Google Scholar

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Claus Michael Ringel
    • 1
  1. 1.Fakultät für Mathematik, UniversitätBielefeld 1Federal Republic of Germany

Personalised recommendations