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Algebras and Representation Theory

, Volume 17, Issue 1, pp 137–159 | Cite as

On Mild Contours in Ray Categories

  • Klaus Bongartz
Article
  • 105 Downloads

Abstract

We generalize and refine the structure and disjointness theorems for non-deep contours obtained in the fundamental article ‘Multiplicative bases and representation-finite algebras’. In particular we show that these contours do not occur in minimal representation-infinite algebras.

Keywords

Cleaving diagrams Non-deep contours Minimal representation-infinite algebras 

Mathematics Subject Classifications (2010)

16G20 16G30 16G60 

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References

  1. 1.
    Bautista, R.: On algebras of strongly unbounded representation type. Comment. Math. Helv. 60, 392–399 (1985)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Bautista, R., Gabriel, P., Roiter, A.V., Salmerón, L.: Representation-finite algebras and multiplicative bases. Invent. Math 81, 217–285 (1985)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Bongartz, K.: Treue einfach zusammenhängende Algebren I. Comment. Math. Helv. 57, 282–330 (1982)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Bongartz, K.: A criterion for finite representation type. Math. Ann. 269, 1–12 (1984)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Bongartz, K.: Critical simply connected algebras. Manuscr. Math. 46, 117–136 (1984)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Bongartz, K.: Indecomposables are standard. Comment. Math. Helv. 60, 400–410 (1985)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Bongartz, K.: Indecomposables live in all smaller lengths. Representat. Theory (2009). arxiv:0904.4609
  8. 8.
    Bongartz, K., Gabriel, P.: Covering spaces in representation theory. Invent. Math 65, 331–378 (1982)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Bongartz, K., Riedtmann, C.: Algèbres stablement héréditaires. C. R. Acad. Sci. Paris Sér. A–B 288(15), 703–706 (1979)zbMATHMathSciNetGoogle Scholar
  10. 10.
    Bretscher, O., Todorov, G.: On a theorem of Nazarova and Roiter. In: Proc. ICRA IV, Lecture Notes 1177, pp. 50–54. (1986)Google Scholar
  11. 11.
    Fischbacher, U.: Une nouvelle preuve d’un théorème de Nazarova et Roiter. (French) A new proof of a theorem of Nazarova and Roiter. C. R. Acad. Sci. Paris Sér. I Math. 300(9), 259–262 (1985)zbMATHMathSciNetGoogle Scholar
  12. 12.
    Fischbacher, U.: Zur Kombinatorik der Algebren mit endlich vielen Idealen. (German) On the combinatorics of algebras with finitely many ideals. J. Reine Angew. Math. 370, 192–213 (1986)zbMATHMathSciNetGoogle Scholar
  13. 13.
    Gabriel, P., Roiter, A.V.: Representations of finite-dimensional algebras. Math. Sci. 73, 1–177 (1992)MathSciNetGoogle Scholar
  14. 14.
    Happel, D., Vossieck, D.: Minimal algebras of infinite representation type with preprojective component. Manuscr. Math. 42, 221–243 (1983)CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    Rogat, A., Tesche, T.: The Gabriel quivers of the sincere simply connected algebras. Diplomarbeit Universität Wuppertal 1992,69 pages, also: SFB-preprint, Ergänzungsreihe 93-005, Bielefeld (1993)Google Scholar
  16. 16.
    Roiter, A.V.: Generalization of Bongartz theorem. In: Math. Inst., pp. 1–32. Ukrainian Acad. of Sciences, Kiev (Preprint, 1981)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.Universität WuppertalWuppertalGermany

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