Advertisement

Auslander-Reiten sequences and representation-finite algebras

  • Peter Gabriel
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 831)

Keywords

Canonical Projection Projective Cover Projective Resolution Injective Hull Oriented Cycle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  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), 269–310MathSciNetCrossRefzbMATHGoogle 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), 306–366MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    Auslander M. and Reiten I., Representation theory of artin algebras III, Comm. Algebra 3 (1975), 239–294MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    Auslander M. and Reiten I., Representation theory of artin algebras IV, Comm. Algebra 5 (1977), 443–518MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    Auslander M. and Reiten I., Representation theory of artin algebras V, Comm. Algebra 5 (1977), 519–554MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    Auslander M. and Reiten I., Representation theory of artin algebras VI, Comm. Algebra 6 (1978), 257–300MathSciNetCrossRefzbMATHGoogle 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), 183–187MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    Butler M.C.R., The construction of almost split sequences, Proc. London Math. Soc., 40 (1980), 72–86MathSciNetCrossRefzbMATHGoogle Scholar
  16. [16]
    Dade E.C., Une extension de la théorie de Hall et Higman, J. of Algebra 20 (1972), 570–609MathSciNetCrossRefzbMATHGoogle 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), 71–103MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    Gabriel P., Indecomposable representations II, Symp. Math. Inst. Naz. Alta Mat. 11 (1973), 81–104.MathSciNetzbMATHGoogle 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), 57–92MathSciNetCrossRefzbMATHGoogle 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), 197–226MathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    Nazarova L.A., The representations of polyquivers of tame type, Zap. Naučn. Sem. LOMI 71 (1977), 181–206MathSciNetzbMATHGoogle 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), 199–224MathSciNetCrossRefzbMATHGoogle 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), 235–255MathSciNetCrossRefzbMATHGoogle 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), 151–165MathSciNetCrossRefzbMATHGoogle Scholar
  35. [35]
    Ulmer F., A flatness criterion in Grothendieck Categories, Invent. Math. 19 (1973), 331–336.MathSciNetCrossRefzbMATHGoogle Scholar
  36. [36]
    Utumi Y., On quotient rings, Osaka Math. J. 8 (1956), 1–18MathSciNetzbMATHGoogle Scholar
  37. [37]
    Yoshii T., On algebras of bounded representation type, Osaka Math. J. 8 (1956), 51–105MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

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

Personalised recommendations