Representation Theory I pp 1-71

Part of the Lecture Notes in Mathematics book series (LNM, volume 831)

Auslander-Reiten sequences and representation-finite algebras

  • Peter Gabriel


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  1. [1]
    Auslancer M., Representation dimension of artin algebras, Queen Mary College Mathematics Notes, London (1971)Google Scholar
  2. [2]
    Auslander M., Representation theory of artin algebras II, Comm. Algebra 1 (1974), 269–310MathSciNetCrossRefMATHGoogle Scholar
  3. [3]
    Auslander M., Applications of morphisms determined by objects, Proc. Conf. on Representation Theory. Philadelphia (1976) Marcel Dekker (1978), 245–327Google Scholar
  4. [4]
    Auslander M. and Reiten I., Stable equivalence of dualizing R-varieties, Adv. in Math. 12 (1974), 306–366MathSciNetCrossRefMATHGoogle Scholar
  5. [5]
    Auslander M. and Reiten I., Representation theory of artin algebras III, Comm. Algebra 3 (1975), 239–294MathSciNetCrossRefMATHGoogle Scholar
  6. [6]
    Auslander M. and Reiten I., Representation theory of artin algebras IV, Comm. Algebra 5 (1977), 443–518MathSciNetCrossRefMATHGoogle Scholar
  7. [7]
    Auslander M. and Reiten I., Representation theory of artin algebras V, Comm. Algebra 5 (1977), 519–554MathSciNetCrossRefMATHGoogle Scholar
  8. [8]
    Auslander M. and Reiten I., Representation theory of artin algebras VI, Comm. Algebra 6 (1978), 257–300MathSciNetCrossRefMATHGoogle Scholar
  9. [9]
    Bautista R., Irreducible maps and the radical of a category, preprintGoogle Scholar
  10. [10]
    Bautista R., Sections in Auslander-Reiten quivers, Proceedings Int. Conf. Rep. Alg., Ottawa 1979Google Scholar
  11. [11]
    Bernstein I.N., Gelfand I.M. and Ponomarjow V.A., Coxeter functors and Gabriel's theorem, Uspechi Mat. Nak. 28 (1973); translated in Rus. Math. Surveys 28 (1973), 17–32Google Scholar
  12. [12]
    Bongartz K., Moduln mit Unterräumen, Diplomarbeit, Bonn (1974)Google Scholar
  13. [13]
    Bongartz K., Zykellose Algebren sind nicht zügellos, Proceedings Int. Conf. Rep. Alg., Ottawa 1979Google Scholar
  14. [14]
    Brenner S. and Butler M.C.R., The equivalence of certain functors occuring in the representation theory of artin algebras and species, J. London Math. Soc. 14 (1976), 183–187MathSciNetCrossRefMATHGoogle Scholar
  15. [15]
    Butler M.C.R., The construction of almost split sequences, Proc. London Math. Soc., 40 (1980), 72–86MathSciNetCrossRefMATHGoogle Scholar
  16. [16]
    Dade E.C., Une extension de la théorie de Hall et Higman, J. of Algebra 20 (1972), 570–609MathSciNetCrossRefMATHGoogle Scholar
  17. [17]
    Dlab V. and Ringel C.M., Indecomposable Representations of graphs and algebras, Mem. Amer. Math. Soc., No. 173, Providence (1976)Google Scholar
  18. [18]
    Donovan P. and Freislich M.R., The representation theory of finite graphs and associated algebras, Carleton Lecture Notes Nr. 5, Ottawa (1973)Google Scholar
  19. [19]
    Gabriel P., Unzerlegbare Darstellungen I, Man. Math. 6 (1972), 71–103MathSciNetCrossRefMATHGoogle Scholar
  20. [20]
    Gabriel P., Indecomposable representations II, Symp. Math. Inst. Naz. Alta Mat. 11 (1973), 81–104.MathSciNetMATHGoogle Scholar
  21. [21]
    Gabriel P., Finite representation type is open, Proc. ICRA 1974, Springer Lecture Notes Nr 488 (1975), 132–155Google Scholar
  22. [22]
    Gelfand I.M. and Ponomarjow V.A., Problems of linear algebra and classification of quadruples in a finite dimensional vector space, Coll. Math. Soc. Bolyai 5, Tihany (1970), 163–237Google Scholar
  23. [23]
    Gelfand I.M. and Ponomarjow V.A., Model algebras and representations of graphs, Funkcional Anal. i Priložen 13 (1979), 1–12MathSciNetCrossRefGoogle Scholar
  24. [24]
    Kac V., Infinite root systems, representations of graphs and invariant theory, Invent. Math. 56 (1980), 57–92MathSciNetCrossRefMATHGoogle Scholar
  25. [25]
    Kupisch H. and Scherzler E., Symmetric algebras of finite representation type, Proc. Int. Conf. Rep. Alg., Ottawa 1979Google Scholar
  26. [26]
    Müller W., Unzerlegbare Moduln über artinschen Ringen, Math. Z. 137 (1974), 197–226MathSciNetCrossRefMATHGoogle Scholar
  27. [27]
    Nazarova L.A., The representations of polyquivers of tame type, Zap. Naučn. Sem. LOMI 71 (1977), 181–206MathSciNetMATHGoogle Scholar
  28. [28]
    Nazarova L.A. and Rojter A.V., Categorical matrix problems and the Brauer-Thrall conjecture, preprint, Inst. Math. Acad. Sci., Kiev 1973, translated in Mitt. Math. Sem. Giessen 115 (1975)Google Scholar
  29. [29]
    Riedtmann Chr., Algebren, Darstellungen, Ueberlagerungen und zurück, Comment. Math.Helv. 55 (1980), 199–224MathSciNetCrossRefMATHGoogle Scholar
  30. [30]
    Riedtmann Chr., Representation-finite selfinjective algebras of class An, Proc. Int. Conf. Rep. Alg., Ottawa (1979)Google Scholar
  31. [31]
    Ringel C.M., Finite-dimensional hereditary algebras of wild representation type, Math. Z. 161 (1978), 235–255MathSciNetCrossRefMATHGoogle Scholar
  32. [32]
    Ringel C.M., The rational invariants of tame quivers, Invent. Math., to appearGoogle Scholar
  33. [33]
    Sélection du Reader's Digest, édition française, No 395, Janvier 1980, 131Google Scholar
  34. [34]
    Storrer H.H., Rings of quotients of perfect rings, Math. Z. 122 (1971), 151–165MathSciNetCrossRefMATHGoogle Scholar
  35. [35]
    Ulmer F., A flatness criterion in Grothendieck Categories, Invent. Math. 19 (1973), 331–336.MathSciNetCrossRefMATHGoogle Scholar
  36. [36]
    Utumi Y., On quotient rings, Osaka Math. J. 8 (1956), 1–18MathSciNetMATHGoogle Scholar
  37. [37]
    Yoshii T., On algebras of bounded representation type, Osaka Math. J. 8 (1956), 51–105MathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Peter Gabriel
    • 1
  1. 1.University of ZurichSwitzerland

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