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Slice modules over minimal 2-fundamental algebras

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Central European Journal of Mathematics

Abstract

We consider a class of algebras whose Auslander-Reiten quivers have starting components that are not generalized standard. For these components we introduce a generalization of a slice and show that only in finitely many cases (up to isomorphism) a slice module is a tilting module.

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References

  1. I. Assem: “Tilting theory — an introduction”, In: Topics in Algebras, Banach Center Publications, Vol. 26, Part I, PWN, Warszawa, 1990, pp. 127–180.

    Google Scholar 

  2. M. Auslander and I. Reiten: “Representation theory of artin algebras III”, Comm. Alg., Vol. 3, (1975), pp. 239–294.

    MathSciNet  MATH  Google Scholar 

  3. M. Auslander and I. Reiten: “Representation theory of artin algebras IV”, Comm. Alg., Vol. 5, (1977), pp. 443–518.

    MathSciNet  MATH  Google Scholar 

  4. M. Auslander, I. Reiten and S.O. Smalø: Representation Theory of Artin Algebras, Cambridge Stud. Adv. Math., Vol. 36, Cambridge Univ. Press, Cambridge, 1995.

    MATH  Google Scholar 

  5. K. Bongartz: Tilted algebras, LNM 903, Springer, Berlin, 1981, pp. 26–38.

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  7. P. Dowbor and A. Skowroński: “Galois coverings of representation-infinite algebras”, Comment. Math. Helv., Vol. 62, (1987), pp. 311–337.

    MathSciNet  MATH  Google Scholar 

  8. P. Gabriel: Auslander-Reiten sequences and representation-finite algebras, INM 831, Springer, Berlin, 1980, pp. 1–71.

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  10. F. Huard: “Tilted gentle algebras”, Comm. Alg., Vol. 26(1), (1998), pp. 63–72.

    MathSciNet  MATH  Google Scholar 

  11. F. Huard and Sh. Liu: “Tilted special biserial algebras”, J. Algebra, Vol. 217, (1999), pp. 679–700.

    Article  MathSciNet  MATH  Google Scholar 

  12. F. Huard and Sh. Liu: “Tilted string algebras”, J. Pure Appl. Algebra, Vol. 153, (2000), pp. 151–164.

    Article  MathSciNet  MATH  Google Scholar 

  13. Z. Pogorzały and M. Sufranek: “Starting and ending components of the Auslander-Reiten quivers of a class of special biserial algebras”, Colloq. Math., Vol. 99(1), (2004), pp. 111–144.

    MathSciNet  MATH  Google Scholar 

  14. C.M. Ringel: Tame algebras and integral quadratic forms, LNM 1099, Springer, Berlin, 1984.

    MATH  Google Scholar 

  15. J. Schröer: “Modules without self-extensions over gentle algebras”, J. Algebra, Vol. 216, (1999), pp. 178–189.

    Article  MathSciNet  MATH  Google Scholar 

  16. A. Skowroński: “Generalized standard Auslander-Reiten components”, J. Math. Soc. Japan, Vol. 46, (1994), pp. 517–543.

    Article  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  18. B. Wald and J. Waschbüsch: “Tame biserial algebras”, J. Algebra, Vol. 95, (1985), pp. 480–500.

    Article  MathSciNet  MATH  Google Scholar 

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Additional information

The first named author was supported by the Polish Scientific Grant KBN No 1 P03A 018 27

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Pogorzały, Z., Szmyt, K. Slice modules over minimal 2-fundamental algebras. centr.eur.j.math. 5, 164–180 (2007). https://doi.org/10.2478/s11533-006-0039-0

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  • DOI: https://doi.org/10.2478/s11533-006-0039-0

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MSC (2000)

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