manuscripta mathematica

, Volume 6, Issue 1, pp 71–103 | Cite as

Unzerlegbare Darstellungen I

  • Peter Gabriel


LetK be the structure got by forgetting the composition law of morphisms in a given category. A linear representation ofK is given by a map V associating with any morphism ϕ: a→e ofK a linear vector space map V(ϕ): V(a)→V(e). We classify thoseK having only finitely many isomorphy classes of indecomposable linear representations. This classification is related to an old paper by Yoshii [3].


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  1. [1]
    CHAPTAL N.: Objets indécomposables dans certaines catégories de foncteurs, C.R. Acad. Sc. Paris, 268, 934–936 (1969).MathSciNetzbMATHGoogle Scholar
  2. [2]
    JANS J.P.: On the indecomposable Representations of Algebras, Ann. of Math., 66, p. 418–429 (1957).MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    YOSHII T.: On Algebras of Bounded Representation Type, Osaka Math. J., 8, 51–105 (1956).MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1972

Authors and Affiliations

  • Peter Gabriel
    • 1
  1. 1.Sonderforschungsbereich “Theoretische Mathematik” Mathematisches InstitutUniversität BonnBonn

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