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References
M. F. Atiyah: On the Krull-Schmidt theorem with applications to sheaves. Bull. Soc. Math. France 84 (1956), 307–317.
M. Auslander, M. I. Platzeck: Representation theory of hereditary artin algebras, in: R. Gordon, Ed., Representation theory of algebras, Marcel Dekker, New York 1978.
M. Auslander, I. Reiten: Representation theory of Artin algebras III. Comm. Alg. 3 (1975), 239–294.
M. Auslander, I. Reiten: Representation theory of Artin algebras V. Comm. Alg. 5 (1977), 519–554 (1977).
D. Baer, W. Geigle, H. Lenzing: The preprojective algebra of a tame hereditary Artin algebra, in preparation.
K. Bongartz: Tilted algebras, in: M. Auslander, E. Lluis, Eds., Representations of algebras, Lecture Notes in Math. 903, Springer (1981), 26–38.
S. Brenner, M. C. R. Butler: Generalization of the Bernstein-Gelfand-Ponomarev reflection functors, in: V. Dlab, P. Gabriel, Eds., Representation theory II, Lecture Notes in Math. 832, Springer (1980), 103–169.
V. Dlab: The regular representations of the tame hereditary algebras, in: Séminaire Dubreil-Malliavin, to appear.
V. Dlab, C. M. Ringel: Indecomposable representations of graphs and algebras. Mem. Amer. Math. Soc. 173 (1976).
V. Dlab, C. M. Ringel: The representations of tame hereditary algebras, in: R. Gordon, Ed., Representation theory of algebras. Marcel Dekker, New York 1978.
V. Dlab, C. M. Ringel: A class of bounded hereditary noetherian domains. J. Algebra, to appear.
P. Gabriel: Des catégories abéliennes. Bull. Soc. Math. France 90 (1962), 323–448.
P. Gabriel: Auslander-Reiten sequences and representation-finite algebras, in: V. Dlab, P. Gabriel, Eds., Representation Theory I, Ottawa 1979, Lecture Notes in Math. 831 (Springer 1980), 1–71.
P. Gabriel, M. Zisman: Calculus of fractions and homotopy theory. Ergebnisse Bd. 35, Springer Berlin-Heidelberg 1967.
W. Geigle: The Krull-Gabriel dimension of the representation theory of a tame hereditary Artin algebra and applications to the structure of exact sequences. manuscripta math. 54, 1–2, 83–106 (1985).
W. Geigle: Krull dimension and Artin algebras. These proceedings.
A. Grothendieck: Sur la classification des fibrés holomorphes sur la surface de Riemann. Amer. J. Math. 79 (1957), 121–138.
D. Happel: Triangulated categories and trivial extension algebras. Preprint 1985.
D. Happel, C. M. Ringel: Tilted algebras. Trans. Amer. Math. Soc. 274 (1982), 399–443.
R. Hartshorne: Algebraic geometry. Springer-Verlag New York-Heidelberg-Berlin 1977.
M. Hazewinkel, C. F. Martin: A short elementary proof of Grothendieck's theorem on algebraic vector bundles over the projective line. J. Pure Applied Algebra 25 (1982), 207–211.
P. J. Hilton and D. Rees: Natural maps of extension functors and a theorem of R. G. Swan, Proc. Cambridge Phil. Soc. 57 (1961), 489–502.
F. Klein: Vorlesungen über das Ikosaeder und die Auflösung der Gleichungen vom fünften Grade. Teubner, Leipzig 1884.
L. Kronecker: Algebraische Reduktion der Scharen bilinearer Formen. Sitzungsberichte Akad. Berlin (1890), 1225–1237.
H. Lenzing: Homological transfer from finitely presented to infinite modules, in: R. Göbel, E. A. Walker, Eds., Abelian group theory, Lecture Notes in Math. 1006. (Springer 1983), 734–761.
H. Lenzing: The pure-projective dimension of torsion-free divisible modules. Comm. Algebra 12 (1984), 649–662.
H. Lenzing: Polyhedral groups and the geometric study of tame hereditary Artin algebras. Preprint.
F. van Oystaeyen, A. Verschoren: Noncommutative algebraic geometry. LNM 887, Springer 1982.
N. Popescu: Abelian categories with applications to rings and modules. Academic Press, London, New York 1973.
C. Riedtmann: Algebren, Darstellungsköcher, überlagerungen und zurück. Comment. Math. Helv. 55 (1980), 199–224.
C. M. Ringel: Infinite dimensional representations of finite dimensional hereditary algebras. Ist. Naz. Alta Mat. Symp. Math. 23 (1979), 321–412.
J.-P. Serre: Faisceaux algébriques cohérents. Ann. of Math. 61 (1955), 197–278.
J.-P. Serre: Géométrie algébrique et géométrie analytique, Ann. Inst. Fourier 6 (1956), 1–42.
H. Tachikawa, T. Wakamatsu: Extensions of tilting functors and QF-3 algebras, Preprint.
W. Geigle, H. Lenzing: Modification of the singularity type for tame hereditary algebras. In preparation.
L.A. Nazarova: Representations of quivers of infinite type. Izv. Akad. Nauk SSR, Ser. Mat. 37 (1973), 752–791.
P. Donovan, M.R. Freislich: The representation theory of finite graphs and associative algebras, Carleton Lecture Notes 5, Ottawa (1973).
W.-D. Geyer: Die Theorie der algebraischen Funktionen einer Veränderlichen nach Dedekind Weber, in: Richard Dedekind, Vieweg Braunschweig 1981, 109–133.
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Lenzing, H. (1986). Curve singularities arising from the representation theory of tame hereditary algebras. In: Dlab, V., Gabriel, P., Michler, G. (eds) Representation Theory I Finite Dimensional Algebras. Lecture Notes in Mathematics, vol 1177. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0075266
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