On tame repetitive algebras

Assem, Ibrahim; Skowroński, Andrzej

Assem, Ibrahim ; Skowroński, Andrzej

Fundamenta Mathematicae, Tome 142 (1993), p. 59-84 / Harvested from The Polish Digital Mathematics Library

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Publié le : 1993-01-01

Zbl 0833.16010

EUDML-ID : urn:eudml:doc:211972

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     author = {Ibrahim Assem and Andrzej Skowro\'nski},
     title = {On tame repetitive algebras},
     journal = {Fundamenta Mathematicae},
     volume = {142},
     year = {1993},
     pages = {59-84},
     zbl = {0833.16010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv142i1p59bwm}
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Assem, Ibrahim; Skowroński, Andrzej. On tame repetitive algebras. Fundamenta Mathematicae, Tome 142 (1993) pp. 59-84. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv142i1p59bwm/

Bibliographie

[00000] [1] I. Assem, Tilted algebras of type $A_{n}$ , Comm. Algebra 10 (1982), 2121-2139. | Zbl 0495.16028

[00001] [2] I. Assem and D. Happel, Generalized tilted algebras of type $A_{n}$ , ibid. 9 (1981), 2101-2125. | Zbl 0481.16009

[00002] [3] I. Assem, D. Happel and O. Roldán, Representation-finite trivial extension algebras, J. Pure Appl. Algebra 33 (1984), 235-242. | Zbl 0564.16027

[00003] [4] I. Assem, J. Nehring and A. Skowroński, Domestic trivial extensions of simply connected algebras, Tsukuba J. Math. 13 (1989), 31-72. | Zbl 0686.16011

[00004] [5] I. Assem and A. Skowroński, Iterated tilted algebras of type $Â_{n}$ , Math. Z. 195 (1987), 269-290. | Zbl 0601.16022

[00005] [6] I. Assem and A. Skowroński, On some classes of simply connected algebras, Proc. London Math. Soc. (3) 56 (1988), 417-450. | Zbl 0617.16018

[00006] [7] I. Assem and A. Skowroński, Algebras with cycle-finite derived categories, Math. Ann. 280 (1988), 441-463. | Zbl 0617.16017

[00007] [8] I. Assem and A. Skowroński, Quadratic forms and iterated tilted algebras, J. Algebra 128 (1990), 55-85. | Zbl 0686.16020

[00008] [9] M. Auslander and I. Reiten, Representation theory of artin algebras III, IV, Comm. Algebra 3 (1975), 239-294 and 5 (1977), 443-518.

[00009] [10] K. Bongartz and P. Gabriel, Covering spaces in representation theory, Invent. Math. 65 (1981/82), 331-378. | Zbl 0482.16026

[00010] [11] S. Brenner and M. Butler, Generalizations of the Bernstein-Gelfand-Ponomarev reflection functors, in: Proc. ICRA II (Ottawa 1979), Lecture Notes in Math. 832, Springer, Berlin 1980, 103-169. | Zbl 0446.16031

[00011] [12] O. Bretscher, C. Läser and C. Riedtmann, Self-injective and simply connected algebras, Manuscripta Math. 36 (1981/82), 253-307. | Zbl 0478.16024

[00012] [13] B. Conti, Simply connected algebras of tree-class $A_{n}$ and $ⅅ_{n}$ , in: Proc. ICRA IV (Ottawa 1984), Lecture Notes in Math. 1177, Springer, Berlin 1986, 60-90.

[00013] [14] V. Dlab and C. M. Ringel, Indecomposable representations of graphs and algebras, Mem. Amer. Math. Soc. 173 (1976).

[00014] [15] P. Dowbor and A. Skowroński, On Galois coverings of tame algebras, Arch. Math. (Basel) 44 (1985), 522-529. | Zbl 0576.16029

[00015] [16] P. Dowbor and A. Skowroński, Galois coverings of representation-infinite algebras, Comment. Math. Helv. 62 (1987), 311-337. | Zbl 0628.16019

[00016] [17] Yu. A. Drozd, Tame and wild matrix problems, in: Proc. ICRA II (Ottawa 1979), Lecture Notes in Math. 832, Springer, Berlin 1980, 242-258.

[00017] [18] P. Gabriel, Auslander-Reiten sequences and representation-finite algebras, in: Proc. ICRA II (Ottawa 1979), Lecture Notes in Math. 831, Springer, Berlin 1980, 1-71.

[00018] [19] P. Gabriel, The universal cover of a representation-finite algebra, in: Proc. ICRA III (Puebla 1980), Lecture Notes in Math. 903, Springer, Berlin 1981, 68-105.

[00019] [20] D. Happel, Tilting sets on cylinders, Proc. London Math. Soc. (3) 51 (1985), 21-55. | Zbl 0583.16020

[00020] [21] D. Happel, On the derived category of a finite-dimensional algebra, Comment. Math. Helv. 62 (1987), 339-389. | Zbl 0626.16008

[00021] [22] D. Happel, J. Rickard and A. Schofield, Piecewise hereditary algebras, Bull. London Math. Soc. 20 (1988), 23-28. | Zbl 0638.16018

[00022] [23] D. Happel and C. M. Ringel, Tilted algebras, Trans. Amer. ath. Soc. 274 (1982), 399-443. | Zbl 0503.16024

[00023] [24] D. Happel and C. M. Ringel, Construction of tilted algebras, in: Proc. ICRA III (Puebla 1980), Lecture Notes in Math. 903, Springer, Berlin 1981, 125-144.

[00024] [25] D. Happel and C. M. Ringel, The derived category of a tubular algebra, in: Proc. ICRA IV (Ottawa 1984), Lecture Notes in ath. 1177, Springer, Berlin 1986, 156-180.

[00025] [26] D. Happel and D. Vossieck, inimal algebras of infinite representation type with preprojective component, Manuscripta ath. 42 (1983), 221-243.

[00026] [27] D. Hughes and J. Waschbüsch, Trivial extensions of tilted algebras, Proc. London Math. Soc. (3) 46 (1983), 347-364. | Zbl 0488.16021

[00027] [28] R. Martínez-Villa and J. A. de la Pe na, The universal cover of a quiver with relations, J. Pure Appl. Algebra 30 (1983), 277-292. | Zbl 0522.16028

[00028] [29] J. Nehring, Polynomial growth trivial extensions of non-simply connected algebras, Bull. Polish Acad. Sci. 36 (1988), 441-445. | Zbl 0777.16008

[00029] [30] J. Nehring and A. Skowroński, Polynomial growth trivial extensions of simply connected algebras, Fund. Math. 132 (1989), 117-134. | Zbl 0677.16008

[00030] [31] C. M. Ringel, Tame algebras, in: Proc. ICRA II (Ottawa 1979), Lecture Notes in Math. 831, Springer, Berlin 1980, 137-287.

[00031] [32] C. M. Ringel, Tame Algebras and Integral Quadratic Forms, Lecture Notes in Math. 1099, Springer, Berlin 1984.

[00032] [33] C. M. Ringel, Representation theory of finite-dimensional algebras, in: Representations of Algebras, Proc. Durham 1985, Cambridge University Press, 1986, 7-80.

[00033] [34] O. Roldán, Tilted algebras of type $\tilde{} A_{n}$ , $\tilde{} B_{n}$ , $\tilde{} C_{n}$ and $\tilde{} B C_{n}$ , Ph.D. thesis, Carleton University, 1983.

[00034] [35] A. Skowroński, Generalization of Yamagata's theorem on trivial extensions, Arch. Math. (Basel) 48 (1987), 68-76. | Zbl 0634.16013

[00035] [36] A. Skowroński, On algebras of finite strong global dimension, Bull. Polish Acad. Sci. 35 (1987), 539-547. | Zbl 0642.16023

[00036] [37] A. Skowroński, Group algebras of polynomial growth, anuscripta Math. 59 (1987), 499-516. | Zbl 0627.16007

[00037] [38] A. Skowroński, Selfinjective algebras of polynomial growth, ath. Ann. 285 (1989), 177-199. | Zbl 0653.16021

[00038] [39] A. Skowroński, Algebras of polynomial growth, in: Topics in Algebra, Banach Center Publ. 26, Part 1, PWN, Warszawa 1990, 535-568.

[00039] [40] A. Skowroński and J. Waschbüsch, Representation-finite biserial algebras, J. Reine Angew. Math. 345 (1983), 172-181. | Zbl 0511.16021

[00040] [41] H. Tachikawa and T. Wakamatsu, Tilting functors and stable equivalences for selfinjective algebras, J. Algebra 109 (1987), 138-165. | Zbl 0616.16012

[00041] [42] H. Tachikawa and T. Wakamatsu, Applications of reflection functors for selfinjective algebras, in: Proc. ICRA IV (Ottawa 1984), Lecture Notes in Math. 1177, Springer, Berlin 1986, 308-327. | Zbl 0572.16019

[00042] [43] J. L. Verdier, Catégories dérivées, état 0, in: SGA 4 1/2, Lecture Notes in Math. 569, Springer, Berlin 1977, 262-311.

[00043] [44] T. Wakamatsu, Stable equivalence between universal covers of trivial extension self-injective algebras, Tsukuba J. Math. 9 (1985), 299-316. | Zbl 0609.16016