References
[B1] Bautista, R.: Irreducible morphisms and the radical of a category. An. Inst. Mat. Univ. Nac. Autónoma México22, 83–135 (1982)
[B2] Bautista, R.: On algebras of strongly unbounded representation type. Comment. Math. Helv. (To appear)
[BLS1] Bautista, R., Larrión, F., Salmerón, L.: On simply connected algebras. J. Lond. Math. Soc. (2),27, 212–220 (1983)
[BLS2] Bautista, R., Larrión, F., Salmerón, L.: Cleaving diagrams in representation theory. (To appear)
[Bo1] Bongartz, K.: Zykellose Algebren sind nicht zügellos. Proc. Ottawa 1979. Springer Lect. Notes 832, pp. 97–102
[Bo2] Bongartz, K.: Treue einfach zusammenhängender Algebren I. Comment. Math. Helv.57, 282–330 (1982)
[Bo3] Bongartz, K.: Algebras and quadratic forms. J. Lond. Math. Soc.28, 461–469 (1983)
[Bo4] Bongartz, K.: A criterion for finite representation type. Math. Ann.269, 1–12 (1984)
[Bo5] Bongartz, K.: Critical simply connected algebras. Manuscr. Math.46, 117–136 (1984)
[Bo6] Bongartz, K.: Indecomposable modules are standard. Comment. Math. Hellv. (To appear)
[BoG] Bongartz, K., Gabriel, P.: Covering spaces in representation theory. Invent. Math.65, 331–378 (1982)
[BrG] Bretscher, O., Gabriel, P.: The standard form of a representation-finite algebra. Bull. Soc. Math. Fr.111, 21–40 (1983)
[EM] Eilenberg, S., Mac Lane, S.: Acyclic models. Am. J. Math.75, 189–199 (1953)
[EZ] Eilenberg, S., Zilber, J.A.: Semi-simplicial complexes and singular homology. Ann. Math.51, 499–513 (1950)
[F1] Fischbacher, U.: The representation-finite algebras with three simple modules. Proceedings of the Fourth Intern. Confer. on Representations of Algebras. Ottawa, Carleton Univ., August 1984
[F2] Fischbacher, U.: Une nouvelle preuve d'un théorème de nazarova et Roiter. Comptes-Rendus Ac. Sc. Paris300, 1–9, 259–263 (1984)
[G1] Gabriel, P.: Unzerlegbare Darstellungen I. Manuscr. Math.6, 71–103 (1972)
[G2] Gabriel, P.: Finite representation type is open. Proc. Ottawa 1974. Springer Lect. Notes 488, pp. 132–155
[G3] Gabriel, P.: Auslander-Reiten sequences and representation finite algebras. Proc. Ottawa 1979. Springer Lect. Notes 831, pp. 1–71
[G4] Gabriel, P.: The universal cover of a representation-finite algebra. Proc. Puebla 1980. Springer Lect. Notes 903, pp. 68–105
[GZ] Gabriel, P., Zisman, M.: Calculus of fractions and Homotopy Theory. In: Ergebnisse der Mathematik, vol. 35. Berlin-Heidelberg-New York: Springer 1967
[HV] Happel, D., Vossieck, D.: Minimal algebras of infinite representation type with preprojective component. Manuscr. Math.42, 221–243 (1983)
[J1] Jans, J.: On the indecomposable representations of algebras. Ann. Math.66, 418–429 (1957)
[J2] Jans, J.: The representation type of algebras and subalgebras. Can. J. Math.10, 39–44 (1958)
[Kf] Kraft, H.: Geometric methods in representation theory. Proc. Puebla 1980. Springer Lect. Notes 944, pp. 180–257
[K1] Kupisch, H.: Symmetrische Algebren mit endlich vielen unzerlegbaren Darstellungen, I, II. J. Reine Angew. Math.219, 1–25 (1965);245, 1–14 (1970)
[K2] Kupisch, H.: Basis-algebren symmetrischer Algebren und eine Vermutung von Gabriel. J. Algebra55, 58–73 (1978)
[KS] Kupisch, H., Scherzler, E.: Symmetric algebras of finite representation type. Proc. Ottawa 1979. Springer Lect. Notes 832, pp. 328–368
[Kg] Krugliak, C.A.: Representations of algebras with zero radical square. Zap. Naučn. Sem. LOMI28, 60–68 (1972)
[ML1] Mac Lane, S.: Homology, 422p. Berlin-Heidelberg-New York: Springer 1970
[ML2] Mac Lane, S.: Categories for the working mathematician, 262p. Berlin-Heidelberg-New York: Springer 1971
[MP1] Martínez-Villa, R., De La Peña, J.A.: Automorphisms of representation-finite algebras. Invent. Math.72, 359–362 (1983)
[MP2] Martínez-Villa, R., De La Peña, J.A.: Multiplicative basis for algebras whose universal cover has no oriented cycle. J. Algebra87, 389–395 (1984)
[Mz1] Mazzola, G.: The algebraic and geometric classification of associative algebras of dimension five. Manuscr. Math.27, 81–101 (1979)
[Mz2] Mazzola, G.: Generic finite schemes and Hochschild cocycles. Comment. Math. Helv.55, 267–293 (1980)
[NR] Nazarova, L.A., Roiter, A.V.: Categorical matrix problems and the Brauer-Thrall conjecture. Preprint Kiev (1973). German version in: Mitt. Math. Semin. Giessen115, 1–153 (1975)
[O] Ovsienko, S.A.: Comments on Roiter's existence proof of multiplicative bases. Private communication (June 1982)
[Re] Reiten, I.: Introduction to the representation theory of Artin algebras. Preprint 67p. University of Trondheim (1983)
[Rd] Riedtmann, Ch.: Many algebras with the same Auslander-Reiten quiver. Bull. London Math. Soc.15, 43–47 (1983)
[Ri] Ringel, C.M.: Indecomposable representations of finite dimensional algebras. Report ICM 82 Warszawa, 14p. (1983)
[R] Roiter, A.V.: Generalization of Bongartz' theorem. Preprint Math. Inst. Ukranian Acad. of Sciences, pp. 1–32, Kiev (1981)
[SW] Skowronski, A., Waschbüsch, J.: Representation finite biserial algebras. J. Reine Angew. Math.345, 172–181 (1983)
[St] Stallings, J.R.: On torsion-free groups with infinitely many ends. Ann. Math.88, 312–334 (1968)
[Sw] Swan, R.G.: Groups of cohomological dimension one. J. Algebra12, 585–601 (1969)
[Vo] Voghera, G.: Zusammenstellung der irreduziblen complexen Zahlensysteme in sechs Einheiten. Denkschr. der math.-naturwiss. Klasse der K. Akademie der Wiss. zu Wien84, 269–328 (1908)
[VW] Von Höhne, H., Waschbüsch, J.: Die StrukturN-reihiger Algebren. Manuskript, Freie Universitat Berlin, 16 S. (1982)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bautista, R., Gabriel, P., Roiter, A.V. et al. Representation-finite algebras and multiplicative bases. Invent Math 81, 217–285 (1985). https://doi.org/10.1007/BF01389052
Issue Date:
DOI: https://doi.org/10.1007/BF01389052