Skip to main content
SpringerLink
Log in

Auslander-Reiten sequences and representation-finite algebras

  • Chapter
  • First Online:
Representation Theory I

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

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. Auslancer M., Representation dimension of artin algebras, Queen Mary College Mathematics Notes, London (1971)

    Google Scholar 

  2. Auslander M., Representation theory of artin algebras II, Comm. Algebra 1 (1974), 269–310

    Article  MathSciNet  MATH  Google Scholar 

  3. Auslander M., Applications of morphisms determined by objects, Proc. Conf. on Representation Theory. Philadelphia (1976) Marcel Dekker (1978), 245–327

    Google Scholar 

  4. Auslander M. and Reiten I., Stable equivalence of dualizing R-varieties, Adv. in Math. 12 (1974), 306–366

    Article  MathSciNet  MATH  Google Scholar 

  5. Auslander M. and Reiten I., Representation theory of artin algebras III, Comm. Algebra 3 (1975), 239–294

    Article  MathSciNet  MATH  Google Scholar 

  6. Auslander M. and Reiten I., Representation theory of artin algebras IV, Comm. Algebra 5 (1977), 443–518

    Article  MathSciNet  MATH  Google Scholar 

  7. Auslander M. and Reiten I., Representation theory of artin algebras V, Comm. Algebra 5 (1977), 519–554

    Article  MathSciNet  MATH  Google Scholar 

  8. Auslander M. and Reiten I., Representation theory of artin algebras VI, Comm. Algebra 6 (1978), 257–300

    Article  MathSciNet  MATH  Google Scholar 

  9. Bautista R., Irreducible maps and the radical of a category, preprint

    Google Scholar 

  10. Bautista R., Sections in Auslander-Reiten quivers, Proceedings Int. Conf. Rep. Alg., Ottawa 1979

    Google Scholar 

  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), 17–32

    Google Scholar 

  12. Bongartz K., Moduln mit Unterräumen, Diplomarbeit, Bonn (1974)

    Google Scholar 

  13. Bongartz K., Zykellose Algebren sind nicht zügellos, Proceedings Int. Conf. Rep. Alg., Ottawa 1979

    Google Scholar 

  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), 183–187

    Article  MathSciNet  MATH  Google Scholar 

  15. Butler M.C.R., The construction of almost split sequences, Proc. London Math. Soc., 40 (1980), 72–86

    Article  MathSciNet  MATH  Google Scholar 

  16. Dade E.C., Une extension de la théorie de Hall et Higman, J. of Algebra 20 (1972), 570–609

    Article  MathSciNet  MATH  Google Scholar 

  17. Dlab V. and Ringel C.M., Indecomposable Representations of graphs and algebras, Mem. Amer. Math. Soc., No. 173, Providence (1976)

    Google Scholar 

  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. Gabriel P., Unzerlegbare Darstellungen I, Man. Math. 6 (1972), 71–103

    Article  MathSciNet  MATH  Google Scholar 

  20. Gabriel P., Indecomposable representations II, Symp. Math. Inst. Naz. Alta Mat. 11 (1973), 81–104.

    MathSciNet  MATH  Google Scholar 

  21. Gabriel P., Finite representation type is open, Proc. ICRA 1974, Springer Lecture Notes Nr 488 (1975), 132–155

    Google Scholar 

  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), 163–237

    Google Scholar 

  23. Gelfand I.M. and Ponomarjow V.A., Model algebras and representations of graphs, Funkcional Anal. i Priložen 13 (1979), 1–12

    Article  MathSciNet  Google Scholar 

  24. Kac V., Infinite root systems, representations of graphs and invariant theory, Invent. Math. 56 (1980), 57–92

    Article  MathSciNet  MATH  Google Scholar 

  25. Kupisch H. and Scherzler E., Symmetric algebras of finite representation type, Proc. Int. Conf. Rep. Alg., Ottawa 1979

    Google Scholar 

  26. Müller W., Unzerlegbare Moduln über artinschen Ringen, Math. Z. 137 (1974), 197–226

    Article  MathSciNet  MATH  Google Scholar 

  27. Nazarova L.A., The representations of polyquivers of tame type, Zap. Naučn. Sem. LOMI 71 (1977), 181–206

    MathSciNet  MATH  Google Scholar 

  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. Riedtmann Chr., Algebren, Darstellungen, Ueberlagerungen und zurück, Comment. Math.Helv. 55 (1980), 199–224

    Article  MathSciNet  MATH  Google Scholar 

  30. Riedtmann Chr., Representation-finite selfinjective algebras of class An, Proc. Int. Conf. Rep. Alg., Ottawa (1979)

    Google Scholar 

  31. Ringel C.M., Finite-dimensional hereditary algebras of wild representation type, Math. Z. 161 (1978), 235–255

    Article  MathSciNet  MATH  Google Scholar 

  32. Ringel C.M., The rational invariants of tame quivers, Invent. Math., to appear

    Google Scholar 

  33. Sélection du Reader's Digest, édition française, No 395, Janvier 1980, 131

    Google Scholar 

  34. Storrer H.H., Rings of quotients of perfect rings, Math. Z. 122 (1971), 151–165

    Article  MathSciNet  MATH  Google Scholar 

  35. Ulmer F., A flatness criterion in Grothendieck Categories, Invent. Math. 19 (1973), 331–336.

    Article  MathSciNet  MATH  Google Scholar 

  36. Utumi Y., On quotient rings, Osaka Math. J. 8 (1956), 1–18

    MathSciNet  MATH  Google Scholar 

  37. Yoshii T., On algebras of bounded representation type, Osaka Math. J. 8 (1956), 51–105

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Zurich, Switzerland

    Peter Gabriel

Authors
  1. Peter Gabriel
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Vlastimil Dlab Peter Gabriel

Rights and permissions

Reprints and permissions

Copyright information

© 1980 Springer-Verlag

About this chapter

Cite this chapter

Gabriel, P. (1980). Auslander-Reiten sequences and representation-finite algebras. In: Dlab, V., Gabriel, P. (eds) Representation Theory I. Lecture Notes in Mathematics, vol 831. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089778

Download citation

  • DOI: https://doi.org/10.1007/BFb0089778

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10263-2

  • Online ISBN: 978-3-540-38385-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation