References
Assem, I.: Tilted algebras of typeA n . Commun. Algebra10, 2121–2139 (1982)
Assem, I.: Torsion theories induced by tilting modules. Can. J. Math.36, 899–913 (1984)
Assem, I., Happel, D.: Generalized tilted algebras of typeA n , Commun. Algebra9, 2101–2125 (1981)
Assem, I., Iwanaga, Y.: Stable equivalence of representation-finite trivial extension algebras. J. Algebra102, 33–38 (1986)
Assem, I., Happel, D., Roldán, O.: Representation-finite trivial extension algebras. J. Pure Appl. Algebra33, 235–242 (1984)
Assem, I., Skowroński, A.: On some classes of simply connected algebras. To appear
Assem, I., Skowroński, A.: Algebras with cycle-finite commun. derived categories. To appear
Auslander, M., Reiten, I.: Representation theory of artin algebras IV, Commun. Algebra5, 443–518 (1977)
Auslander, M., Reiten, I.: Representation theory of artin algebras VI. Commun. Algebra6, 257–300 (1978)
Auslander, M., Platzeck, M.I., Reiten, I.: Coxeter functors without diagrams. Trans. Am. Math. Soc.250, 1–46 (1979)
Bautista, R.: Sections in Auslander-Reiten quivers. Proc. ICRA II (Ottawa, 1979). Springer Lecture Notes No.832, 74–96 (1980)
Bongartz, K.: Tilted algebras. Proc. ICRA III Puebla, 1980), Springer Lecture Notes No.903, 26–38.
Bongartz, K., Gabriel, P.: Covering spaces in representation theory. Invent. Math.65, 331–378 (1981/82)
Bretscher, O., Gabriel, P.: The standard form of a representation-finite algebra. Bull. Soc. Math. France111, 21–40 (1983)
Dlab, V., Ringel, C.M.: Indecomposable representations of graphs and algebras. Mem. Am. Math. Soc., No.173, Providence (1976)
Dowbor, P., Skowroński, A.: On Galois coverings of tame algebras. Arch. Math.44, 522–529 (1985)
Gabriel, P.: Auslander-Reiten sequences and representation-finite algebras. Proc. ICRA II (Ottawa, 1979), Springer Lecture Notes No.831, 1–71 (1980)
Happel, D.: Tilting sets on cylinders. Proc. London Math. Soc. (3),51, 21–55 (1985)
Happel, D.: On the derived category of a finite-dimensional algebra. To appear in Comment. Math. Helv.
Happel, D.: Iterated tilted algebras of affine type. Commun. Algebra15, 29–45 (1987)
Happel, D., Ringel, C.M.: Tilted algebras. Trans. Am. Math. Soc.274, 399–443 (1982)
Hoshino, M.: DTr-invariant modules. Tsukuba J. Math.7, 205–214 (1983)
Hughes, D., Waschbüsch, J.: Trivial extensions of tilted algebras. Proc. London Math. Soc. (3)46, 347–364 (1983)
Martinez-Villa, R., de la Peña, J.A.: The universal cover of a quiver with relations. J. Pure Appl. Algebra30, 277–292 (1983)
de la Peña, J.A.: Representation-finite algebras whose Auslander-Reiten quiver is planar. J. London Math. Soc. (2)32, 62–74 (1985)
Pogorzaly, Z., Skowroński, A.: On algebras whose indecomposable modules are multiplicityfree. Proc. London Math. Soc.47, 463–479 (1983)
Ringel, C.M.: Finite-dimensional hereditary algebras of wild representation type. Math. Z.161, 235–255 (1978)
Ringel, C.M.: Tame algebras. Proc. Workshop ICRA II (Ottawa, 1979). Springer Lecture Notes No.831, 137–287 (1980)
Ringel, C.M.: Tame algebras and integral quadratic forms. Springer Lecture Notes No.1099 (1984)
Roldán, O.: Tilted algebras of types\(\tilde {\mathbb{A}}_n ,\tilde {\mathbb{B}}_n ,\tilde {\mathbb{C}}_n and \tilde {\mathbb{B}\mathbb{C}}_n\). Ph.D. Thesis, Carleton University (1983)
Simson, D., Skowroński, A.: Extensions of artinian rings by hereditary injective modules. Proc. ICRA III (Puebla, 1980). Springer Lecture Notes No.903, 315–330 (1981)
Skowroński, A.: A characterization of a new class of artin algebras. J. London Math. Soc. (2)26, 53–63 (1982)
Skowroński, A.: On nonexistence of oriented cycles in Auslander-Reiten quivers. Acta Univ. Carolinae, Vol.25, No. 1, 45–52 (1984)
Skowroński, A.: Generalization of Yamagata's theorem on trivial extensions. Arch. Math.48, 68–76 (1987)
Skowroński, A., Waschbüsch, J.: Representation-finite biserial algebras. J. Reine Angew. Math.345, 172–181 (1983)
Tachikawa, H., Wakamatsu, T.: Tilting functors and stable equivalences for self-injective algebras. To appear in J. Algebra
Verdier, J.L.: Catégories dérivées, état 0. Springer Lecture Notes569, 262–311 (1977)
Wald, B., Waschbüsch, J.: Tame biserial algebras. J. Algebra95, 480–500 (1985)
Yamagata, K.: On algebras whose trivial extensions are of finite representation type. Proc. ICRA III (Puebla, 1980). Springer Lecture Notes No.903, 364–371 (1981)
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This paper was written while the authors were visiting the University of Bielefeld as Alexander von Humboldt fellows
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Assem, I., Skowroński, A. Iterated tilted algebras of type\(\tilde {\mathbb{A}}_n \) . Math Z 195, 269–290 (1987). https://doi.org/10.1007/BF01166463
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DOI: https://doi.org/10.1007/BF01166463