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Covering spaces in representation-theory. (English) Zbl 0482.16026


MSC:

16G70 Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers
16G60 Representation type (finite, tame, wild, etc.) of associative algebras
16P10 Finite rings and finite-dimensional associative algebras

Citations:

Zbl 0444.16018

References:

[1] Auslander, M.: Representation theory of artin algebras II. Comm. Algebra1, 269-310 (1974) · Zbl 0285.16029 · doi:10.1080/00927877409412807
[2] Auslander, M., Reiten, I.: Representation theory of artin algebras V. Comm. Algebra5, 519-554 (1977) · Zbl 0396.16008 · doi:10.1080/00927877708822181
[3] Bautista, R.: Irreducible maps and the radical of a category. Preprint. Mexico 1979 · Zbl 0461.16023
[4] Bongartz, K.: Tilted algebras. Preprint. To appear in Proc. of the third Int Conf. on Rep. of Alg. Puebla 1980 · Zbl 0478.16025
[5] Bongartz, K., Ringel, C.M.: Representation-finite tree algebras. Preprint. To appear in Proc. of the third Int. Conf. on Rep. of Alg., Puebla 1980 · Zbl 0479.16024
[6] Gabriel, P.: Chr. Riedtmann and the selfinjective alebras.of finite representation-type, Proc. Conf. on Ring Theory, Antwerp 1978. New York Basel: Marcel Dekker 1979
[7] Gabriel, P.: Auslander-Reiten sequences and representation-finite algebras. In: Rep. Theory I, Proc. of the Workshop on the pres. Trends in Rep. Theory., Ottawa 1979, Lecture Notes 831, 1-71. Berlin Heidelberg New York: Springer 1980
[8] Gabriel, P., Zisman, M.: Calculus of fractions and Homotopy Theory. Erg. Math.35, Berlin Heidelberg New York: Springer 1967 · Zbl 0186.56802
[9] Happel, D., Ringel, C.M.: Tilted algebras. Report at the third Int. Conf. on Rep. of Alg., Puebla 1980. To appear in Trans. Amer. Math. Soc. · Zbl 0503.16024
[10] Kleiner, M.M.: Partially ordered sets of finite type. Zap. Nau?. Sem. LOMI28, 32-41 (1972) · Zbl 0345.06001
[11] Loupias, M.: Représentations indécomposables des ensembles ordonnés finis. Thèse, Université de Tours, 1975
[12] Mac Lane, S.: Homology. Grundlehren114. Berlin Heidelberg New York: Springer 1963
[13] Nazarova, L.A., Roijter, A.V.: Representations of partially ordered sets. Zap. Nau?n. Sem. LOMI28, 5-31 (1972)
[14] Nikulin, A.V., Panasiuk, C.A.: Representations of algebras with two non-isomorphic indecomposable projective representations (russian). To appear in Dokl. Ak. Nauk USSR
[15] Riedtmann, Chr.: Algebren, Darstellungsköcher, Überlagerungen und zurück. Comm. Math. Helv.55, 199-224 (1980) · Zbl 0444.16018 · doi:10.1007/BF02566682
[16] Riedtmann, Chr: Representation-finite selfinjective algebras of classA n . In: Rep. Theory II, Proc. of the second Int. Conf. on Rep. of Alg., Ottawa 1979, Springer Lecture Notes832, 449-520. Berlin Heidelberg New York: Springer 1980
[17] Ringel, C.M.: Report on the Brauer-Thrall conjectures: Roijter’s theorem and the theorem of Nazarova and Roijter. In: Rep. Theory I, Proc. of the Workshop on the present Trends. In: Rep. Theor. Ottawa 1979. Springer Lecture Notes831, 104-136. Berlin Heidelberg New York: Springer 1979
[18] Ringel, C.M.: Tame algebras. In: loc. cit. Springer Lecture Notes831, 137-287. Berlin Heidelberg New York: Springer 1979
[19] ?kabara, A.S., Zavadskij, A.G.: Commutative quivers and matrix algebras of finite type. Preprint. Kiev 1976
[20] Spanier, E.H.: Algebraic Topology. Mc Graw-Hill, New York 1966 · Zbl 0145.43303
[21] Assem, I., Happel, D.: Generalized Tilted Algebras of TypeA n . Carleton Mathematical Series 171. Carleton University, Ottawa Dec. 1980
[22] Comtet, L.: Advanced Combinatorics. D. Reidel Publ. Comp., Dordrecht-Holland 1974
[23] Happel, D., Ringel, C.M.: Construction of tilted algebras. Preprint. University of Bielefeld, Oct. 1980 · Zbl 0503.16025
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