On the numbers of discrete indecomposable modules over tame algebras

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1. [1] I. Assem and A. Skowroński, On some classes of simply connected algebras, Proc. London Math. Soc. 56 (1988), 417-450. Zbl0617.16018
2. [2] I. Assem and A. Skowroński, Indecomposable modules over multicoil algebras, Math. Scand. 71 (1992), 31-61. Zbl0796.16014
3. [3] I. Assem and A. Skowroński, Multicoil algebras, in: Representations of Algebras, Sixth Internat. Conf. Ottawa 1992, CMS Conf. Proc. 14, Amer. Math. Soc., 1993, 29-68. Zbl0827.16010
4. [4] I. Assem, A. Skowroński and B. Tomé, Coil enlargements of algebras, Tsukuba J. Math. 19 (1995), 453-479. Zbl0860.16014
5. [5] M. Auslander, M. I. Platzeck and I. Reiten, Coxeter functors without diagrams, Trans. Amer. Math. Soc. 250 (1979), 1-20. 
6. [6] M. Auslander and I. Reiten, Modules determined by their composition factors, Illinois J. Math. 29 (1985), 280-301. Zbl0539.16011
7. [7] M. Auslander, I. Reiten and S. O. Smalø, Representation Theory of Artin Algebras, Cambridge Stud. Adv. Math. 36, Cambridge Univ. Press, 1995. Zbl0834.16001
8. [8] K. Bongartz, Algebras and quadratic forms, J. London Math. Soc. 28 (1983), 461-469. Zbl0532.16020
9. [9] K. Bongartz and P. Gabriel, Covering spaces in representation theory, Invent. Math. 65 (1982), 331-378. Zbl0482.16026
10. [10] W. W. Crawley-Boevey, On tame algebras and bocses, Proc. London Math. Soc. 56 (1988), 451-483. Zbl0661.16026
11. [11] Yu. A. Drozd, Tame and wild matrix problems, in: Representation Theory II, Second Internat. Conf. Ottawa 1979, Lecture Notes in Math. 832, Springer, 1980, 242-258. 
12. [12] M. Harada and Y. Sai, On categories of indecomposable modules I, Osaka J. Math. 7 (1970), 323-344. Zbl0248.18018
13. [13] M. Hoshino, Modules without self-extensions and Nakayama's conjecture, Arch. Math. (Basel) 43 (1984), 493-500. Zbl0547.16014
14. [14] S. Liu, Infinite radicals in standard Auslander-Reiten components, J. Algebra 166 (1994), 245-254. Zbl0809.16016
15. [15] R. Nörenberg and A. Skowroński, Tame minimal non-polynomial growth simply connected algebras, Colloq. Math., to appear. Zbl0889.16005
16. [16] J. A. de la Peña, On the dimension of the module-varieties of tame and wild algebras, Comm. Algebra 19 (1991), 1795-1807. Zbl0818.16013
17. [17] J. A. de la Peña and A. Skowroński, Geometric and homological characterizations of polynomial growth simply connected algebras, Invent. Math., in press. Zbl0883.16007
18. [18] I. Reiten, A. Skowroński and S. O. Smalø, Short chains and short cycles of modules, Proc. Amer. Math. Soc. 117 (1993), 343-354. Zbl0794.16013
19. [19] C. M. Ringel, Finite dimensional hereditary algebras of wild representation type, Math. Z. 161 (1978), 235-255. Zbl0415.16023
20. [20] C. M. Ringel, Report on the Brauer-Thrall conjectures, in: Representation Theory I, Second Internat. Conf. Ottawa 1979, Lecture Notes in Math. 831, Springer, 1980, 104-136. 
21. [21] C. M. Ringel, Tame Algebras and Integral Quadratic Forms, Lecture Notes in Math. 1099, Springer, 1984. 
22. [22] A. Skowroński, Algebras of polynomial growth, in: Topics in Algebra, Banach Center Publ. 26, Part I, PWN, Warszawa, 1990, 535-568. 
23. [23] A. Skowroński, Simply connected algebras and Hochschild cohomologies, in: Representations of Algebras, Sixth Internat. Conf. Ottawa 1992, CMS Conf. Proc. 14, Amer. Math. Soc., 1993, 431-447. Zbl0806.16012
24. [24] A. Skowroński, Generalized standard Auslander-Reiten components without oriented cycles, Osaka J. Math. 30 (1993), 515-527. Zbl0818.16017
25. [25] A. Skowroński, Generalized standard Auslander-Reiten components, J. Math. Soc. Japan 46 (1994), 517-543. Zbl0828.16011
26. [26] A. Skowroński, On the composition factors of periodic modules, J. London Math. Soc. 49 (1994), 477-492. Zbl0819.16012
27. [27] A. Skowroński, Cycles in module categories, in: Finite Dimensional Algebras and Related Topics, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 424, Kluwer, 1994, 309-345. Zbl0819.16013
28. [28] A. Skowroński, Criteria for polynomial growth of algebras, Bull. Polish Acad. Sci. Math. 4 (1994), 157-163. Zbl0865.16011
29. [29] A. Skowroński, Module categories over tame algebras, in: Representation Theory of Algebras and Related Topics, Proc. Workshop Mexico 1994, CMS Conf. Proc. 19, Amer. Math. Soc., 1996, 281-313. Zbl0856.16010
30. [30] A. Skowroński, Simply connected algebras of polynomial growth, Compositio Math., in press. Zbl0889.16004
31. [31] Y. Zhang, The modules in any component of the AR-quiver of a wild hereditary artin algebra are uniquely determined by their composition factors, Arch. Math. (Basel) 53 (1989), 250-251. Zbl0651.16013
32. [32] G. Zwara, Degenerations in the module varieties of generalized standard Auslander-Reiten components, Colloq. Math. 72 (1997), 281-303. Zbl0890.16006

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