Download PDF - On the numbers of discrete indecomposable modules over tame algebrasAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

On the numbers of discrete indecomposable modules over tame algebras

Authors 1, 1

Affiliations

  1. Faculty of Mathematics and Informatics, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

Bibliography

  1. I. Assem and A. Skowroński, On some classes of simply connected algebras, Proc. London Math. Soc. 56 (1988), 417-450.
  2. I. Assem and A. Skowroński, Indecomposable modules over multicoil algebras, Math. Scand. 71 (1992), 31-61.
  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.
  4. I. Assem, A. Skowroński and B. Tomé, Coil enlargements of algebras, Tsukuba J. Math. 19 (1995), 453-479.
  5. M. Auslander, M. I. Platzeck and I. Reiten, Coxeter functors without diagrams, Trans. Amer. Math. Soc. 250 (1979), 1-20.
  6. M. Auslander and I. Reiten, Modules determined by their composition factors, Illinois J. Math. 29 (1985), 280-301.
  7. M. Auslander, I. Reiten and S. O. Smalø, Representation Theory of Artin Algebras, Cambridge Stud. Adv. Math. 36, Cambridge Univ. Press, 1995.
  8. K. Bongartz, Algebras and quadratic forms, J. London Math. Soc. 28 (1983), 461-469.
  9. K. Bongartz and P. Gabriel, Covering spaces in representation theory, Invent. Math. 65 (1982), 331-378.
  10. W. W. Crawley-Boevey, On tame algebras and bocses, Proc. London Math. Soc. 56 (1988), 451-483.
  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. M. Harada and Y. Sai, On categories of indecomposable modules I, Osaka J. Math. 7 (1970), 323-344.
  13. M. Hoshino, Modules without self-extensions and Nakayama's conjecture, Arch. Math. (Basel) 43 (1984), 493-500.
  14. S. Liu, Infinite radicals in standard Auslander-Reiten components, J. Algebra 166 (1994), 245-254.
  15. R. Nörenberg and A. Skowroński, Tame minimal non-polynomial growth simply connected algebras, Colloq. Math., to appear.
  16. J. A. de la Peña, On the dimension of the module-varieties of tame and wild algebras, Comm. Algebra 19 (1991), 1795-1807.
  17. J. A. de la Peña and A. Skowroński, Geometric and homological characterizations of polynomial growth simply connected algebras, Invent. Math., in press.
  18. I. Reiten, A. Skowroński and S. O. Smalø, Short chains and short cycles of modules, Proc. Amer. Math. Soc. 117 (1993), 343-354.
  19. C. M. Ringel, Finite dimensional hereditary algebras of wild representation type, Math. Z. 161 (1978), 235-255.
  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. C. M. Ringel, Tame Algebras and Integral Quadratic Forms, Lecture Notes in Math. 1099, Springer, 1984.
  22. A. Skowroński, Algebras of polynomial growth, in: Topics in Algebra, Banach Center Publ. 26, Part I, PWN, Warszawa, 1990, 535-568.
  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.
  24. A. Skowroński, Generalized standard Auslander-Reiten components without oriented cycles, Osaka J. Math. 30 (1993), 515-527.
  25. A. Skowroński, Generalized standard Auslander-Reiten components, J. Math. Soc. Japan 46 (1994), 517-543.
  26. A. Skowroński, On the composition factors of periodic modules, J. London Math. Soc. 49 (1994), 477-492.
  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.
  28. A. Skowroński, Criteria for polynomial growth of algebras, Bull. Polish Acad. Sci. Math. 4 (1994), 157-163.
  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.
  30. A. Skowroński, Simply connected algebras of polynomial growth, Compositio Math., in press.
  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.
  32. G. Zwara, Degenerations in the module varieties of generalized standard Auslander-Reiten components, Colloq. Math. 72 (1997), 281-303.
Colloquium Mathematicum
1997/73/1
Export to PBN, Opens in new tab
Pages:
93-114
Main language of publication
English
Received
1996-06-27
Accepted
1996-08-14
Published
1997
Exact and natural sciences