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Algèbres auto-injectives de représentation finie (d'après Christine Riedtmann)

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Séminaire Bourbaki vol. 1979/80 Exposés 543 – 560

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 842))

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Bibliographie

  1. AUSLANDER M.: Representation theory of Artin algebras II, Comm. Algebra (1974), 269–310

    Google Scholar 

  2. AUSLANDER M. and REITEN I.: Representation theory of algebras III, Comm. Algebra (1975),239–294.

    Google Scholar 

  3. AUSLANDER M. and REITEN I.: Representation theory of algebras IV, Comm. Algebra (1977), 443–518.

    Google Scholar 

  4. AUSLANDER M. and REITEN I.: Representation theory of algebras VI, Comm. Algebra (1978)

    Google Scholar 

  5. AUSLANDER M. and REITEN I.: Stable equivalence of Artin algebras, Proc. Conf. on Orders, group rings and related topics, Springer Lecture Notes No 353,8–71.

    Google Scholar 

  6. BAUTISTA R.: Irreducible maps and the radical of a category, preprint

    Google Scholar 

  7. BERNSTEIN I.N., GEL'FAND I.M. and PONOMARJOV V.A.: Coxeter functors and Gabriel's theorem, translated in Russian Math. Surveys 28 (1973), 17–32.

    MATH  Google Scholar 

  8. BONGARTZ K.: Zykellose Algebren sind nicht zügellos, Proceedings of the 2nd Int. Conf. on Rep. of Alg., Ottawa 1979, to appear in Springer Lecture Notes.

    Google Scholar 

  9. CURTIS C.W. and REINER I.: Representation Theory of Finite Groups and Associative Algebras, Wiley, New York 1962.

    MATH  Google Scholar 

  10. DADE E.C.: Blocks with cyclic defect groups, Ann. of Math. 84 (1966), 20–48

    Article  MATH  MathSciNet  Google Scholar 

  11. DLAB V. and RINGEL C.M.: Indecomposable representations of graphs and algebras, Memoirs Amer. Math. Soc. No 173, Providence (1976).

    Google Scholar 

  12. GABRIEL P.: Des catégories abéliennes, Bull. Soc. Math. Fr. (1962), 323–448

    Google Scholar 

  13. GABRIEL P.: Indecomposable representations II, Symp. Math. Ist. Naz. Alta Mat. (1973), 81–104

    Google Scholar 

  14. GABRIEL P. and RIEDTMANN Chr.: Group representations without groups, Comm. Math. Helv. (1979), 240–287.

    Google Scholar 

  15. GEL'FAND I.M. and PONOMARJOV V.A.: Model algebras and representations of graphs (russian), Funct. Anal. 13 (1979), 1–12.

    Article  MATH  Google Scholar 

  16. GREEN J.A.: Walking around the Brauer tree, J. Austral. Math. Soc. 17 (1974), 197–213.

    Article  MATH  MathSciNet  Google Scholar 

  17. HIGMAN D.G.: Indecomposable representations at characteristic p, Duke Math. J. 21 (1954), 377–381.

    Article  MATH  MathSciNet  Google Scholar 

  18. JANUSZ G.J.: Indecomposable Modules for finite groups, Ann. of Math. 89 (1969), 209–241.

    Article  MATH  MathSciNet  Google Scholar 

  19. KASCH F., KNESER M. und KUPISCH H.: Unzerlegbare modulare Darstellungen endlicher Gruppen mit zyklischer p-Sylow-Gruppe, Arch. Math. 8(1957), 320–321.

    Article  MATH  MathSciNet  Google Scholar 

  20. KUPISCH H.: Projektive Moduln endlicher Gruppen mit zyklischer p-Sylow-Gruppe, J. of Alg. 10 (1968), 1–7.

    Article  MATH  MathSciNet  Google Scholar 

  21. KUPISCH H.: Unzerlegbare Moduln endlicher Gruppen mit zyklischer p-Sylow-Gruppe, Math. Z. 108 (1969) 77–104.

    Article  MATH  MathSciNet  Google Scholar 

  22. KUPISCH H.: Basisalgebren symmetrischer Algebren und eine Vermutung von Gabriel, Math. Z. (to appear)

    Google Scholar 

  23. KUPISCH H.: Quasi-Frobenius algebras of finite representation type, Proceedings of the 2nd Int. Conf. on Rep. of Alg., Ottawa 1979, to appear in Springer Lecture Notes.

    Google Scholar 

  24. LOUPIAS M.: Représentations indécomposables des ensembles ordonnés finis, Thèse 1975 (Tours).

    Google Scholar 

  25. MICHLER G.: Green correspondence between blocks with cyclic defect groups I, J. of Alg. 39 (1976), 26–51.

    Article  MATH  MathSciNet  Google Scholar 

  26. PEACOCK R.M.: Blocks with a cyclic defect group, J. of Alg. 34 (1975), 232–259.

    Article  MATH  MathSciNet  Google Scholar 

  27. RIEDTMANN Chr.: Algebren, Darstellungsköcher, Ueberlagerungen und zurück, to appear in Comm. Math. Helv. (1979).

    Google Scholar 

  28. RIEDTMANN Chr.: Representation-finite self-injective algebras of class An and Dn, Proceedings of the 2nd Int. Conf. on Rep. of Alg., Ottawa 1979, to appear in Springer Lecture Notes.

    Google Scholar 

  29. RIEDTMANN Chr.: Representation-finite self-injective algebras of class E6, E7 and E8, to appear.

    Google Scholar 

  30. SCHERZLER E. and WASCHBUESCH J.: A class of self-injective algebras of finite representation type, Proc. of the 2nd Int. Conf. on Rep. of Alg., Ottawa 1979, to appear in Springer Lecture Notes.

    Google Scholar 

  31. STORRER H.H.: Rings of quotients of perfect rings, Math. Z. 122 (1971), 151–165.

    Article  MATH  MathSciNet  Google Scholar 

  32. ULMER F.: A flatness criterion in Grothendieck Categories, Inventiones 19 (1973), 331–336

    Article  MATH  MathSciNet  Google Scholar 

  33. ZAVADSKIJ A.G. and NAZAROVA L.A.: Partially ordered sets of tame type, in Matrix problems (russian), Kiev 1978.

    Google Scholar 

  34. ECKMANN B.: Homotopie et dualité, Col. de Top. Alg., Louvain 1956, 41–53.

    Google Scholar 

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Authors and Affiliations

  1. Mathematisches Institut, Universität Zürich, Freiestrasse 36, 8032, Zürich

    Pierre Gabriel

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  1. Pierre Gabriel
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© 1981 N. Bourbaki

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Gabriel, P. (1981). Algèbres auto-injectives de représentation finie (d'après Christine Riedtmann). In: Séminaire Bourbaki vol. 1979/80 Exposés 543 – 560. Lecture Notes in Mathematics, vol 842. Springer, Berlin, Heidelberg . https://doi.org/10.1007/BFb0089926

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  • DOI: https://doi.org/10.1007/BFb0089926

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  • Print ISBN: 978-3-540-10292-2

  • Online ISBN: 978-3-540-38437-3

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