This is a preview of subscription content, log in via an institution to check access.
Bibliography
[AH]Assem, I. andHappel, D., Generalized tilted algebras of typeA n , Comm. Algebra,9 (1981), 2101–2125.
[AB]Auslander, M. andBridger, M.,Stable module theory, Mem. Amer. Math. Soc., No. 94, Providence (1969).
[AR]Auslander, M. andReiten, I.,Representation theory of Artin Algebras III, VI, Comm. Algebra3 (1975), 239–294,5 (1977) 443–518.
[APR]Auslander, M., Platzeck, M. I. andReiton, I.,Coxetor functors without diagrams, Trans. Amer. Math. Soc. 250 (1979), 1–46.
[BLS]Bautista, R., Larrión, F. andSalmerón, L.,On simply connected algebras, J. London Math. Soc., Vol. 27, Part 2 (1983), 212–220.
[B1]Beilinson, A. A., Coherent sheaves on ℙn and problems of linear algebra, Func. Anal. and Appl., Vol. 12, No. 3, 214–216.
[B2]Beilinson, A. A., The derived category of Coherent Sheaves on ℙn, Sel. Math. Sov., Vol. 3, No. 3, 1983/84, 233–237.
[BBD]Beilinson, A. A., Bernstein, J. andDeligne, P.,Faisceaux pervers, Astérique (100), 1982.
[BGG]Bernstein, I. N., Gel'fand, I. M. andGel'fand, S. I., Algebraic bundles over ℙn and problems of linear algebra, Func. Anal. and Appl., Vol. 12, No. 3, 212–214.
[BGP]Bernstein, I. N., Gel'fand, I. M. andPonomarev, V. A.,Coxeter functors and Gabriel's theorem, Uspecki Mat. Nauk.28 (1973), translated in Russian Math. Surveys28 (1973), 17–32.
[Bo1]Bongartz, K.,Tilted algebras, Springer Lecture Notes 903 (1982), 26–38.
[Bo2]Bongartz, K.,A criterion for finite representation type, Math. Ann.269 (1984), 1–12.
[BG]Bongartz, K. andGabriel, P.,Covering spaces in representation theory, Invent. Math.65 (1981), 331–378.
[BB]Brenner, S. andButler, M. C. R.,Generalization of the Bernstein-Gel'fand-Ponomarev reflection functors, Springer Lecture Notes832 (1980), 103–169.
[BrG]Bretscher, O. andGabriel, P.,The standard form of a representation-finite algebra, Bull. Soc. Math. France, 111 (1983), 21–40.
[DR]Dlab, V. andRingel, C. M.,Indecomposable representations of graphs and algebras, Mem. Amer. Math. Soc., No. 173, Providence (1973).
[G1]Gabriel, P.,Unzerlegbare Darstellungen I, Manuscripta Math.6 (1972), 71–102.
[G2]Gabriel, P.,Auslander-Reiten sequences and representation-finite algebras, Springer Lecture Notes831 (1980), 1–71.
[G3]Gabriel, P.,The universal cover of a representation-finite algebra, Springer Lecture Notes903 (1981), 68–105.
[Gr]Grothendieck, A.,Groupes des classes des catégories abeliennes et triangulées. Complexes parfait, in SGA 5, Exposé VIII, Springer Lecture Notes589 (1977).
[H1]Happel, D.,Composition factors for indecomposable modules, Proc. Amer. Math. Soc.86 (1982), 29–31.
[H2]Happel, D.,Tilting sets on cylinders, Proc. London Math. Soc. (3),51 (1985), 21–55.
[H3]Happel, D.,Iterated tilted algebras of affine type, to appear Comm of Alg.
[HR]Happel, D. andRingel, C. M.,Tilted algebras, Trans. Amer. Math. Soc.,274 (2), (1982), 399–443.
[Ha]Hartshorne, R.,Residues and Duality, Springer Lecture Notes 20 (1966).
[He]Heller, A.,The loop-space functor in homological algebra. Trans. Amer. Math. Soc.96 (1960), 382–394.
[HW]Hughes, D. andWaschbüsch, J.,Trivial extensions of tilted algebras, Proc. London Math. Soc. (3),46 (1983), 347–364.
[ML]Mac Lane, S.,Categories for the working mathematician, Springer Verlag 1971.
[Q]Quillen, D.,Higher algebraic K-theory I, Springer Lecture Notes341 (1973), 85–147.
[R]Riedtmann, C.,Algebren, Darstellungsköcher, Überlagerungen und zurück, Comm. Math. Helv.55 (1980), 199–224.
[Ri]Ringel, C. M.,Representations of K-species and bimodules, J. Algebra41 (1976), 269–302.
[Ri2]Ringel, C. M.,Finite dimensional hereditary algebras of wild representation type, Math. Z.161 (1978), 235–255.
[Ri3]Ringel, C. M.,Report on the Brauer-Thrall Conjectures, Springer Lecture Notes831 (1980), 104–136, and Tame algebras, same volume, 137–287.
[Ri4]Ringel, C. M.,The rational invariants of tame quivers, Invent. Math.58, (1980), 217–239.
[Ri5]Ringel, C. M.,Bricks in hereditary length categories, Resultate der Mathematik6(1), (1983), 64–70.
[Ri6]Ringel, C. M.,Tame algebras and quadratic forms, Springer Lecture Notes1099 (1984).
[TW]Tachikawa, H., andWakamatsu, T.,Applications of reflection functors for selfinjective algebras, Proc. ICRA IV, Carleton Lecture Notes, 1984.
[V]Verdier, J. L.,Catégories dérivés, état 0, Springer Lecture Notes569 (1977), 262–311.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Happel, D. On the derived category of a finite-dimensional algebra. Commentarii Mathematici Helvetici 62, 339–389 (1987). https://doi.org/10.1007/BF02564452
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02564452