Skip to main content
Log in

Indecomposables in Derived Categories of Gentle Algebras

  • Published:
Algebras and Representation Theory Aims and scope Submit manuscript

Abstract

We give a description of the indecomposable objects in the derived category of a finite-dimensional gentle algebra.

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. Assem, I. and Skowro?sky, A.: Iterated tilted algebras of type \(\tilde {\mathbb{A}}\) n, Math. Z. 195 (1987), 269–290.

    Google Scholar 

  2. Bondarenko, V. M.: Representations of dihedral groups over a field of characteristic 2, Mat. Sb. 96 (1) (1975), 63–74; English translation: Math. USSR Sb. 25 (1975), 58–68.

    Google Scholar 

  3. Bondarenko, V. M. and Drozd, Yu. A.: Representation type of finite groups, Zap. Nauchn. Sem. LOMY 57 (1977), 24–41; English translation: J. Soviet Math. 20 (1982), 2515–2528.

    Google Scholar 

  4. Grivel, P.-P.: Catégories dérivées et foncteurs dérivés, In: A. Borel et al. (eds), Algebraic D-modules, Academic Press, New York, 1987.

    Google Scholar 

  5. Gabriel, P. and Roiter, A.: Representations of finite-dimensional algebras, Algebra VIII, Encyclopaedia of Math. Sci. 73, Springer, New York, 1992.

    Google Scholar 

  6. Drozd, Yu. A.: Tame and wild matrix problems, In: Representations and Quadratic Forms, Institute of Mathematics, Academy of Sciences, Ukrainian SSR, Kiev, 1979, pp. 39–74, Amer. Math. Soc. Transl. 128 (1986), 31–55.

    Google Scholar 

  7. Happel, D.: Triangulated Categories in the Representation Theory of Finite Dimensional Algebras, London Math. Soc. Lecture Notes Ser. 119, Cambridge Univ. Press, 1988.

  8. Hartshorne, R.: Residues and Dualities, Lecture Notes in Math. 20, Springer, New York, 1966.

    Google Scholar 

  9. Geiss, Ch. and Krause, H.: On the notion of derived tameness, Preprint 2000, www.matem.unam.mx/christof/preprints/derived.ps.

  10. König, S. and Zimmermann, A.: Derived Equivalences for Group Rings, Lecture Notes in Math. 1685, Springer, New York, 1998.

    Google Scholar 

  11. Nazarova, L. A. and Roiter, A. V.: On a problem of Gel'fand, Funktsional. Anal. i Prilozhen. 7 (1973), 54–69.

    Google Scholar 

  12. Ringel, C. M.: Tame Algebras and Integral Quadratic Forms, Lecture Notes in Math. 1099, Springer, New York, 1984.

    Google Scholar 

  13. Ringel, C. M.: The repetitive algebra of a gentle algebra, Bol. Soc. Mat. Mexicana 3(3) (1997), 235–253.

    Google Scholar 

  14. Vossieck, D.: The algebras with discrete derived category, in preparation.

  15. Weibel, C. A.: An Introduction to Homological Algebra, Cambridge Stud. Adv. Math. 38, Cambridge Univ. Press, 1994.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bekkert, V., Merklen, H.A. Indecomposables in Derived Categories of Gentle Algebras. Algebras and Representation Theory 6, 285–302 (2003). https://doi.org/10.1023/A:1025142023594

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1025142023594

Navigation