Skip to main content
Log in

Generalization of Yamagata's theorem on trivial extensions

  • Published:
Archiv der Mathematik Aims and scope Submit manuscript

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.

References

  1. I. Assem, D. Happel andO. Roldán, Representation-finite trivial extension algebras. J. Pure Appl. Algebra33, 235–242 (1984).

    Google Scholar 

  2. K. Bongartz, Tilted algebras. In: Representations of Algebras. LNM903, 26–38, Berlin-Heidelberg-New York 1981.

    Google Scholar 

  3. K. Bongartz andP. Gabriel, Covering spaces in representation theory. Invent. Math.65, 331–378 (1982).

    Google Scholar 

  4. S. Brenner andM. C. R. Butler, Generalization of the Bernstein-Gelfand-Ponomarev reflection functors. In: Representation Theory II. LNM832, 103–169, Berlin-Heidelberg-New York 1980.

    Google Scholar 

  5. P. Dowbor andA. Skowroński, Galois coverings of tame algebras. Arch. Math.44, 522–529 (1985).

    Google Scholar 

  6. P. Dowbor, H. Lenzing andA. Skowroński, Galois coverings of algebras by locally supportfinite categories. In: Representation Theory I. Finite dimensional algebras. LNM1177, 91–93, Berlin-Heidelberg-New York-Tokyo 1986.

    Google Scholar 

  7. P.Dowbor and A.Skowroński, Galois coverings of representation-infinite algebras. Preprint.

  8. R. M.Fossum, P. A.Griffith and I.Reiten, Trivial extensions of abelian categories. LNM456, Berlin-Heidelberg-New York 1975.

  9. P. Gabriel, Auslander-Reiten sequences and representation-finite algebras. In: Representation Theory I. LNM831, 1–71, Berlin-Heidelberg-New York 1980.

    Google Scholar 

  10. P. Gabriel, The universal cover of a representation-finite algebra. In: Representations of Algebras. LNM903, 68–105, Berlin-Heidelberg-New York 1981.

    Google Scholar 

  11. D.Happel, On the derived category of a finite dimensional algebra. Preprint.

  12. D. Happel andC. M. Ringel, Tilted algebras. Trans. Amer. Math. Soc.274, 339–443 (1982).

    Google Scholar 

  13. D. Happel andC. M. Ringel, The derived category of a tubular algebra. In: Representation Theory I. Finite dimensional algebras. LNM1177, 156–180, Berlin-Heidelberg-New York-Tokyo 1986.

    Google Scholar 

  14. M. Harada andY. Sai, On the categories of indecomposable modules I. Osaka J. Math.7, 323–344 (1970).

    Google Scholar 

  15. A. Heller, The loop-space functor in homological algebra. Trans. Amer. Math. Soc.96, 382–394 (1960).

    Google Scholar 

  16. D. Hughes andJ. Waschbüsch, Trivial extensions of tilted algebras. Proc. London Math. Soc.46, 347–364 (1983).

    Google Scholar 

  17. Y. Iwanaga andT. Wakamatsu, Trivial extensions of artin algebras. In: Representation Theory II. LNM832, 295–301, Berlin-Heidelberg-New York 1980.

    Google Scholar 

  18. S.Mac Lane, Categories for the working mathematician. Berlin-Heidelberg-New York 1971.

  19. C. M. Ringel, Report on the Brauer-Thrall conjectures. In: Representation Theory I. LNM831, 104–136, Berlin-Heidelberg-New York 1980.

    Google Scholar 

  20. C. M.Ringel, Tame algebras and integral quadratic forms. LNM1099, Berlin-Heidelberg-New York-Tokyo 1984.

  21. D. Simson andA. Skowroński, Extensions of artinian rings by hereditary injective modules. In: Representations of Algebras. LNM903, 315–330, Berlin-Heidelberg-New York 1981.

    Google Scholar 

  22. A. Skowroński, A characterization of a new class of artin algebras. J. London Math. Soc.26, 53–63 (1982).

    Google Scholar 

  23. H. Tachikawa, Representations of trivial extensions of hereditary algebras. In: Representation Theory II. LNM832, 579–599, Berlin-Heidelberg-New York 1980.

    Google Scholar 

  24. H. Tachikawa, Selfinjective algebras and tilting theory. In: Representation Theory I. Finite dimensional algebras. LNM1177, 272–307, Berlin-Heidelberg-New York-Tokyo 1986.

    Google Scholar 

  25. J. L. Verdier, Catégories dérivées, état 0. In: Cohomologie Etale. LNM569, 262–312, Berlin-Heidelberg-New York 1977.

    Google Scholar 

  26. K. Yamagata, On algebras whose trivial extensions are of finite representation type. In: Representations of Algebras. LNM903, 364–371, Berlin-Heidelberg-New York 1981.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

The paper was written while the author was visiting the Bielefeld University. He was supported by Deutsche Forschungsgemeinschaft and Alexander von Humboldt-Stiftung.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Skowroński, A. Generalization of Yamagata's theorem on trivial extensions. Arch. Math 48, 68–76 (1987). https://doi.org/10.1007/BF01196357

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01196357

Keywords

Navigation