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References
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.
AUSLANDER, M., PLATZECK, M.I. and REITEN, I.: Coxeter functors without diagrams, Trans. A.M.S., 250 (1979), 1–46.
AUSLANDER, M. and REITEN, I.: Representation theory of artin algebras, Parts I–VI, Communications in Algebra, 1974–1978.
BAUTISTA, R.: Classification of certain algebras of finite representation type, Communication Interna, No.51, 1978, Departmento de Matematicas, Facultad de Ciencias, UNAM.
BAUTISTA, R.: Sections in Auslander-Reiten quivers, preprint, 1979.
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).
BRENNER, S.: Quivers with commutativity conditions and some phenomenology of forms, Proc. ICRA 1974, Springer Lecture Notes 488, 29–53.
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.
CARTAN, H. and EILENBERG, S.: Homological algebra. Princeton University Press, 1956.
DLAB, V. and RINGEL, C.M.: Indecomposable representations of graphs and algebras, Memoirs A.M.S., No.173, (1976).
DONOVAN, P. and FREISLICH, M.R.: Indecomposable representations of certain commutative quivers, Bull. Austral. Math. Soc. 20 (1979), 17–34.
GABRIEL, P.: Representations indecomposable, Seminaire Bourbaki (1973/74), Exp. 444.
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.
HUGHES, D.W.: Private communication.
KAC, V.G.: Infinite root systems, representations of graphs, and invariant theory, preprint, 1979.
KAC, V.G.: Infinite root systems, representations of quivers, and invariant theory, This Proceedings.
LOUPIAS, M.: Representations indecomposable des ensembles ordonnes finis, These, Universite Tours, 1975. (Summary: Proc. ICRA, 1974, Springer Lecture Notes 488, 201–209.)
MARMARIDIS, N.: Darstellungen endlichen Ordnungen, Dissertation, Universität Zürich, 1978.
MARMARIDIS, N.: Reflection functors, This Proceedings.
NAZAROVA, L.A. and ROITER, A.V.: On a problem of I.M. Gelfand, Funkc. Anal. i Prilozen. 7 (1973), 54–69.
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.
RINGEL, C.M.: Representations of K-species and bimodules, J. Algebra 41 (1976), 269–302.
RINGEL, C.M.: This Proceedings.
SHKABARA, A.S.: Commutative quivers of tame type, I, preprint, Kiev, 1978.
ZAVADSKI, A.G.: Quivers with a distinguished path and no cycles which are of tame type, preprint, Kiev, 1978.
ZAVADSKI, A.G. and SHKABARA, A.S.: Commutative quivers and matrix algebras of finite type, preprint, Kiev, 1976.
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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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