Skip to main content
Log in

Classification of discrete derived categories

  • Published:
Central European Journal of Mathematics

Abstract

The main aim of the paper is to classify the discrete derived categories of bounded complexes of modules over finite dimensional algebras.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. I. Assem and D. Happel: “Generalized tilted algebras of type\(\mathbb{A}_n \)”, Comm. Algebra, Vol. 9, (1981), pp. 2101–2125.

    MathSciNet  MATH  Google Scholar 

  2. I. Assem and A. Skowroński: “Iterated tilted algebras of type \( \tilde{\mathbb{A}}_n\) ”, Math. Z., Vol. 195, (1987), pp. 269–290.

    Article  MathSciNet  MATH  Google Scholar 

  3. I. Assem and A. Skowroński: “Algebras with cycle-finite derived categories”, Math. Ann., Vol. 280, (1988), pp. 441–463.

    Article  MathSciNet  MATH  Google Scholar 

  4. M. Auslander, M. Platzeck and I. Reiten: “Coxeter functors without diagrams”, Trans. Amer. Math. Soc., Vol. 250, (1979), pp. 1–46.

    Article  MathSciNet  MATH  Google Scholar 

  5. M. Barot and J. A. de la Peña: “The Dynkin type of non-negative unit form”, Expo. Math., Vol. 17, (1999), pp. 339–348.

    MATH  Google Scholar 

  6. K. Bongartz: “Tilted Algebras”, Lecture Notes in Math., Vol. 903, (1981), pp. 26–38.

    MathSciNet  Google Scholar 

  7. K. Bongartz and P. Gabriel: “Covering spaces in representation theory”, Invent. Math., Vol. 65, (1981), pp. 331–378.

    Article  MathSciNet  Google Scholar 

  8. M. C. R. Butler and C. M. Ringel: “Auslander-Reiten sequences with few middle terms and applications to string algebras”, Comm. Algebra, Vol. 15, (1987), pp. 145–179.

    MathSciNet  MATH  Google Scholar 

  9. Ch. Geiß and J. A. de la Peña: “Auslander-Reiten components for clans”, Bol. Soc. Mat. Mexicana, Vol. 5, (1999), pp. 307–326.

    MathSciNet  MATH  Google Scholar 

  10. D. Happel: Triangulated categories in the representation theory of finite-dimensional algebras, London Math. Soc. Lecture Note Series, 1988.

  11. D. Happel: “Auslander-Reiten triangles in derived categories of finite-dimensional algebras”, Proc. Amer. Math. Soc., Vol. 112, (1991), pp. 641–648.

    Article  MathSciNet  MATH  Google Scholar 

  12. D. Happel and C. M. Ringel: “Tilted algebras”, Trans. Amer. Math. Soc., Vol. 274, (1982), pp. 399–443.

    Article  MathSciNet  MATH  Google Scholar 

  13. D. Hughes and J. Waschbüsch: “Trivial extensions of tilted algebras”, Proc. London Math. Soc., Vol. 46, (1983), pp. 347–364.

    MathSciNet  MATH  Google Scholar 

  14. B. Keller and D. Vossieck: “Aisles in derived, categories”, Bull. Soc. Math. Belg., Vol. 40, (1988), pp. 239–253.

    MathSciNet  MATH  Google Scholar 

  15. J. Nehring: “Polynomial growth trivial extensions of non-simply connected algebras”, Bull. Polish Acad. Sci. Math., Vol. 36, (1988), pp. 441–445.

    MathSciNet  MATH  Google Scholar 

  16. J. Rickard: “Morita theory for derived categories”, J. London Math. Soc., Vol. 39, (1989), pp. 436–456.

    MathSciNet  MATH  Google Scholar 

  17. C. M. Ringel: Tame Algebras and Integral Quadratic Forms, Lecture Notes in Math., 1984.

  18. C. M. Ringel: “The repetitive algebra of a gentle algebra”, Bol. Soc. Mat. Mexicana, Vol. 3, (1997), pp. 235–253.

    MathSciNet  MATH  Google Scholar 

  19. A. Skowroński and J. Waschbüsch: “Representation-finite biserial algebras”, J. Reine Angew. Math., Vol. 345, (1983), pp. 172–181.

    MathSciNet  MATH  Google Scholar 

  20. J. L. Verdier: “Categories derivées, état 0”, Lecture Notes in Math., Vol. 569, (1977), pp. 262–331.

    MathSciNet  Google Scholar 

  21. D. Vossieck: “The algebras with discrete derived category”, J. Algebra, Vol. 243, (2001), pp. 168–176.

    Article  MathSciNet  MATH  Google Scholar 

  22. H. Tachikawa and T. Wakamatsu: “Applications of reflection functors for selfinjective algebras”, Lecture Notes in Math., Vol. 1177, (1986), pp. 308–327.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

About this article

Cite this article

Bobiński, G., Geiß, C. & Skowroński, A. Classification of discrete derived categories. centr.eur.j.math. 2, 19–49 (2004). https://doi.org/10.2478/BF02475948

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.2478/BF02475948

Keywords

MSC (2000)

Navigation