Keywords
- Finite Length
- Dynkin Diagram
- Global Section
- Path Algebra
- Coherent Sheave
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
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.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1986 Springer-Verlag
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/BFb0075266
Received:
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-16432-6
Online ISBN: 978-3-540-39776-2
eBook Packages: Springer Book Archive
