On tame repetitive algebras

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1. [1] I. Assem, Tilted algebras of type $A_n$, Comm. Algebra 10 (1982), 2121-2139. Zbl0495.16028
2. [2] I. Assem and D. Happel, Generalized tilted algebras of type $A_n$, ibid. 9 (1981), 2101-2125. Zbl0481.16009
3. [3] I. Assem, D. Happel and O. Roldán, Representation-finite trivial extension algebras, J. Pure Appl. Algebra 33 (1984), 235-242. Zbl0564.16027
4. [4] I. Assem, J. Nehring and A. Skowroński, Domestic trivial extensions of simply connected algebras, Tsukuba J. Math. 13 (1989), 31-72. Zbl0686.16011
5. [5] I. Assem and A. Skowroński, Iterated tilted algebras of type ${Â}_n$, Math. Z. 195 (1987), 269-290. Zbl0601.16022
6. [6] I. Assem and A. Skowroński, On some classes of simply connected algebras, Proc. London Math. Soc. (3) 56 (1988), 417-450. Zbl0617.16018
7. [7] I. Assem and A. Skowroński, Algebras with cycle-finite derived categories, Math. Ann. 280 (1988), 441-463. Zbl0617.16017
8. [8] I. Assem and A. Skowroński, Quadratic forms and iterated tilted algebras, J. Algebra 128 (1990), 55-85. Zbl0686.16020
9. [9] M. Auslander and I. Reiten, Representation theory of artin algebras III, IV, Comm. Algebra 3 (1975), 239-294 and 5 (1977), 443-518. 
10. [10] K. Bongartz and P. Gabriel, Covering spaces in representation theory, Invent. Math. 65 (1981/82), 331-378. Zbl0482.16026
11. [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. Zbl0446.16031
12. [12] O. Bretscher, C. Läser and C. Riedtmann, Self-injective and simply connected algebras, Manuscripta Math. 36 (1981/82), 253-307. Zbl0478.16024
13. [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. 
14. [14] V. Dlab and C. M. Ringel, Indecomposable representations of graphs and algebras, Mem. Amer. Math. Soc. 173 (1976). 
15. [15] P. Dowbor and A. Skowroński, On Galois coverings of tame algebras, Arch. Math. (Basel) 44 (1985), 522-529. Zbl0576.16029
16. [16] P. Dowbor and A. Skowroński, Galois coverings of representation-infinite algebras, Comment. Math. Helv. 62 (1987), 311-337. Zbl0628.16019
17. [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. 
18. [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. 
19. [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. 
20. [20] D. Happel, Tilting sets on cylinders, Proc. London Math. Soc. (3) 51 (1985), 21-55. Zbl0583.16020
21. [21] D. Happel, On the derived category of a finite-dimensional algebra, Comment. Math. Helv. 62 (1987), 339-389. Zbl0626.16008
22. [22] D. Happel, J. Rickard and A. Schofield, Piecewise hereditary algebras, Bull. London Math. Soc. 20 (1988), 23-28. Zbl0638.16018
23. [23] D. Happel and C. M. Ringel, Tilted algebras, Trans. Amer. ath. Soc. 274 (1982), 399-443. Zbl0503.16024
24. [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. 
25. [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. 
26. [26] D. Happel and D. Vossieck, inimal algebras of infinite representation type with preprojective component, Manuscripta ath. 42 (1983), 221-243. 
27. [27] D. Hughes and J. Waschbüsch, Trivial extensions of tilted algebras, Proc. London Math. Soc. (3) 46 (1983), 347-364. Zbl0488.16021
28. [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. Zbl0522.16028
29. [29] J. Nehring, Polynomial growth trivial extensions of non-simply connected algebras, Bull. Polish Acad. Sci. 36 (1988), 441-445. Zbl0777.16008
30. [30] J. Nehring and A. Skowroński, Polynomial growth trivial extensions of simply connected algebras, Fund. Math. 132 (1989), 117-134. Zbl0677.16008
31. [31] C. M. Ringel, Tame algebras, in: Proc. ICRA II (Ottawa 1979), Lecture Notes in Math. 831, Springer, Berlin 1980, 137-287. 
32. [32] C. M. Ringel, Tame Algebras and Integral Quadratic Forms, Lecture Notes in Math. 1099, Springer, Berlin 1984. 
33. [33] C. M. Ringel, Representation theory of finite-dimensional algebras, in: Representations of Algebras, Proc. Durham 1985, Cambridge University Press, 1986, 7-80. 
34. [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. 
35. [35] A. Skowroński, Generalization of Yamagata's theorem on trivial extensions, Arch. Math. (Basel) 48 (1987), 68-76. Zbl0634.16013
36. [36] A. Skowroński, On algebras of finite strong global dimension, Bull. Polish Acad. Sci. 35 (1987), 539-547. Zbl0642.16023
37. [37] A. Skowroński, Group algebras of polynomial growth, anuscripta Math. 59 (1987), 499-516. Zbl0627.16007
38. [38] A. Skowroński, Selfinjective algebras of polynomial growth, ath. Ann. 285 (1989), 177-199. Zbl0653.16021
39. [39] A. Skowroński, Algebras of polynomial growth, in: Topics in Algebra, Banach Center Publ. 26, Part 1, PWN, Warszawa 1990, 535-568. 
40. [40] A. Skowroński and J. Waschbüsch, Representation-finite biserial algebras, J. Reine Angew. Math. 345 (1983), 172-181. Zbl0511.16021
41. [41] H. Tachikawa and T. Wakamatsu, Tilting functors and stable equivalences for selfinjective algebras, J. Algebra 109 (1987), 138-165. Zbl0616.16012
42. [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. Zbl0572.16019
43. [43] J. L. Verdier, Catégories dérivées, état 0, in: SGA 4 1/2, Lecture Notes in Math. 569, Springer, Berlin 1977, 262-311. 
44. [44] T. Wakamatsu, Stable equivalence between universal covers of trivial extension self-injective algebras, Tsukuba J. Math. 9 (1985), 299-316. Zbl0609.16016

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