manuscripta mathematica

, Volume 61, Issue 2, pp 183–194 | Cite as

On the representation type of one point extensions of tame concealed algebras

  • J. A. de la Peña
Article

Abstract

Letk be an algebraically closed field and Λ a finite dimensionalk-algebra. LetqΛ be the quadratic Tits form associated with Λ. If Λ is tame we show thatqΛ is weakly semipositive. Let Λ be a one-point extension of a tame concealed algebra, then Λ is tame iffqΛ is weakly semipositive.

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References

  1. [1]
    Assem I. and Skowronski A.: On some classes of simply connected algebras. Preprint. Bielefeld (1986)Google Scholar
  2. [2]
    Auslander M. and Reiten I.: Representation theory of Artin algebras III, Comm. Alg.3, 239–294 (1975)Google Scholar
  3. [3]
    Bautista R., Larrión F. and Salmerón L.: On simply connected algebras, J. London Math. Soc. (2),27, 212–220 (1983)Google Scholar
  4. [4]
    Bongartz K.: Algebras and quadratic forms, J. London Math. Soc.28, 461–469 (1983)Google Scholar
  5. [5]
    Bongartz K.: A criterion for finite representation type. Math. Ann.269, 1–12 (1984)Google Scholar
  6. [6]
    Crawley-Boevey W. W.: On tame algebras and Bocses. Preprint. Liverpool (1987)Google Scholar
  7. [7]
    Dlab V. and Ringel C. M.: Indecomposable representations of graphs and algebras, Memoirs Amer. Math. Soc.173, 1–57 (1976)Google Scholar
  8. [8]
    Drozd J.: Tame and wild matrix problems. In Representation theory II. Springer LNM 832, 242–258 (1980) On tame and wild matrix problems, in Matrix Problems, Kiev, 104–114 (1977)Google Scholar
  9. [9]
    Gabriel P.: Auslander-Reiten sequences and representation-finite algebras. In Representation theory I. Springer LNM 831, 1–71 (1980)Google Scholar
  10. [10]
    Happel D. and Ringel C. M.: Tilted algebras, Trans. Amer. Math. Soc.274, 399–443 (1982)Google Scholar
  11. [11]
    Happel D. and Vossieck D.: Minimal algebras of infinite representation-type with preprojective component, Manuscripta Math.42, 221–243 (1983)Google Scholar
  12. [12]
    Marmaridis N.: One point extensions of trees and quadratic forms. Preprint. Greece (1987)Google Scholar
  13. [13]
    Nazarova L. A.: The representation of partially ordered sets of infinite type. Izv. Akad. Nauk SSSR. Ser. Math.39, 963–991 (1975)Google Scholar
  14. [14]
    de la Peña J. A. and Tomé B.: Iterated tubular algebras. Preprint, México (1987)Google Scholar
  15. [15]
    Ringel C. M.: Tame algebras. In Representation theory I. Springer LNM 831, 137–287 (1980)Google Scholar
  16. [16]
    Ringel C. M.: Tame algebras and quadratic forms. Springer LNM 1099, (1984)Google Scholar
  17. [17]
    Roiter A. V.: Representation of posets and tame matrix problems. In Representation theory of Algebras. London Math. Soc. LNM 6, 91–107 (1986)Google Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • J. A. de la Peña
    • 1
  1. 1.Instituto de Matemáticas Area de la Investigación Cientifíca Circuito ExteriorCiudad UniversitariaMéxico 04510 D. F.México

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