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Representation Theory II pp 103–169Cite as

Generalizations of the Bernstein-Gelfand-Ponomarev reflection functors

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References

  1. AUSLANDER, M. and PLATZECK, M.I.: Representation theory of hereditary artin algebras, Lecture Notes in Pure and Appl. Math., vol.37, 389–424, Dekker, New York, 1978.

    MathSciNet  MATH  Google Scholar 

  2. AUSLANDER, M., PLATZECK, M.I. and REITEN, I.: Coxeter functors without diagrams, Trans. A.M.S., 250 (1979), 1–46.

    Article  MathSciNet  MATH  Google Scholar 

  3. AUSLANDER, M. and REITEN, I.: Representation theory of artin algebras, Parts I–VI, Communications in Algebra, 1974–1978.

    Google Scholar 

  4. BAUTISTA, R.: Classification of certain algebras of finite representation type, Communication Interna, No.51, 1978, Departmento de Matematicas, Facultad de Ciencias, UNAM.

    Google Scholar 

  5. BAUTISTA, R.: Sections in Auslander-Reiten quivers, preprint, 1979.

    Google Scholar 

  6. BERNSTEIN, I.N., GELFAND, I.M. and PONOMAREV, V.A.: Coxeter functors and Gabriel’s theorem, Uspechi Mat. Nauk. 28, 19–38, (1973) = Russian Math. Surveys 28, 17–32 (1973).

    MathSciNet  MATH  Google Scholar 

  7. BRENNER, S.: Quivers with commutativity conditions and some phenomenology of forms, Proc. ICRA 1974, Springer Lecture Notes 488, 29–53.

    Google Scholar 

  8. BRENNER, S. and BUTLER, M.C.R.: The equivalence of certain functors occurring in the representation theory of artin algebras and species, J. London Math. Soc. (2) 14 (1976), 207–215.

    Article  MathSciNet  MATH  Google Scholar 

  9. CARTAN, H. and EILENBERG, S.: Homological algebra. Princeton University Press, 1956.

    Google Scholar 

  10. DLAB, V. and RINGEL, C.M.: Indecomposable representations of graphs and algebras, Memoirs A.M.S., No.173, (1976).

    Google Scholar 

  11. DONOVAN, P. and FREISLICH, M.R.: Indecomposable representations of certain commutative quivers, Bull. Austral. Math. Soc. 20 (1979), 17–34.

    Article  MathSciNet  MATH  Google Scholar 

  12. GABRIEL, P.: Representations indecomposable, Seminaire Bourbaki (1973/74), Exp. 444.

    Google Scholar 

  13. GELFAND, I.M. and PONOMAREV, V.A.: Problems of linear algebra and the classification of quadruples of subspaces in a finite-dimensional vector space, Coll. Math. Soc. Bolyai 5, Tihany (1970), 163–237.

    Google Scholar 

  14. HUGHES, D.W.: Private communication.

    Google Scholar 

  15. KAC, V.G.: Infinite root systems, representations of graphs, and invariant theory, preprint, 1979.

    Google Scholar 

  16. KAC, V.G.: Infinite root systems, representations of quivers, and invariant theory, This Proceedings.

    Google Scholar 

  17. LOUPIAS, M.: Representations indecomposable des ensembles ordonnes finis, These, Universite Tours, 1975. (Summary: Proc. ICRA, 1974, Springer Lecture Notes 488, 201–209.)

    Google Scholar 

  18. MARMARIDIS, N.: Darstellungen endlichen Ordnungen, Dissertation, Universität Zürich, 1978.

    Google Scholar 

  19. MARMARIDIS, N.: Reflection functors, This Proceedings.

    Google Scholar 

  20. NAZAROVA, L.A. and ROITER, A.V.: On a problem of I.M. Gelfand, Funkc. Anal. i Prilozen. 7 (1973), 54–69.

    MathSciNet  Google Scholar 

  21. NAZAROVA, L.A. and ROITER, A.V.: Categorical matrix problems and the Brauer-Thrall conjecture, Inst. Math. Acad. Sc., Ukr. SSR, Kiev, 1973. = (German translation) Mitteilungen Mathem. Seminar Giessen, Heft 15, 1975.

    Google Scholar 

  22. RINGEL, C.M.: Representations of K-species and bimodules, J. Algebra 41 (1976), 269–302.

    Article  MathSciNet  MATH  Google Scholar 

  23. RINGEL, C.M.: This Proceedings.

    Google Scholar 

  24. SHKABARA, A.S.: Commutative quivers of tame type, I, preprint, Kiev, 1978.

    Google Scholar 

  25. ZAVADSKI, A.G.: Quivers with a distinguished path and no cycles which are of tame type, preprint, Kiev, 1978.

    Google Scholar 

  26. ZAVADSKI, A.G. and SHKABARA, A.S.: Commutative quivers and matrix algebras of finite type, preprint, Kiev, 1976.

    Google Scholar 

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Authors and Affiliations

  1. Departments of Mathematics, The University, P.O. Box 147, L69 3BX, Liverpool, England

    Sheila Brenner & M. C. R. Butler

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  1. Sheila Brenner
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  2. M. C. R. Butler
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Vlastimil Dlab Peter Gabriel

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© 1980 Springer-Verlag

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Brenner, S., Butler, M.C.R. (1980). Generalizations of the Bernstein-Gelfand-Ponomarev reflection functors. In: Dlab, V., Gabriel, P. (eds) Representation Theory II. Lecture Notes in Mathematics, vol 832. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0088461

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  • DOI: https://doi.org/10.1007/BFb0088461

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10264-9

  • Online ISBN: 978-3-540-38387-1

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