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Simply connected algebras of polynomial growth

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Compositio Mathematica

Abstract

The representation theory of polynomial growth strongly simply connected finite dimensional algebras over an algebraically closed field is established.

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References

  1. Assem, I. and Skowroński, A.: On some classes of simply connected algebras, Proc. London Math. Soc.56 (1988) 417–450.

    Google Scholar 

  2. Assem, I. and Skowroński, A.: Minimal representation-infinite coil algebras, Manuscripta Math.67 (1990) 305–331.

    Google Scholar 

  3. Assem, I. and Skowroński, A.: Indecomposable modules over multicoil algebras, Math. Scand.71 (1992) 31–61.

    Google Scholar 

  4. Assem, I. and Skowroński, A.: Multicoil algebras, in: Representations of Algebras, CMS Conf. Proc.14 (1993) 29–68.

    Google Scholar 

  5. Assem, I, Skowroński, A. and Tomé, B.: Coil enlargement of algebras, Tsukuba J. Math.19 (1995) 453–479.

    Google Scholar 

  6. Auslander, M., Platzeck, M. I. and Reiten, I.: Coxeter functors without diagrams, Trans. Amer. Math. Soc.250 (1979) 1–46.

    Google Scholar 

  7. Bautista, R., Gabriel, P., Roiter, A. V. and Salmeron, L.: Representation-finite algebras and multiplicative bases, Invent. Math.81 (1985) 217–285.

    Google Scholar 

  8. Bautista, R., Larrion, F. and Salmeron, L.: On simply connected algebras, J. London Math. Soc.27 (1983) 212–220.

    Google Scholar 

  9. Bongartz, K. On a result of Bautista and Smalø on cycles, Comm. Algebra11 (1983) 2123–2124.

    Google Scholar 

  10. Bongartz, K.: Treue einfach zusammenhängende Algebren I, Comment. Math. Helv.57 (1982) 282–330.

    Google Scholar 

  11. Bongartz, K.: Algebras and quadratic forms, J. London Math. Soc.28 (1983) 461–469.

    Google Scholar 

  12. Bongartz, K.: Critical simply connected algebras, Manuscripta Math.46 (1984) 117–136.

    Google Scholar 

  13. Bongartz, K.: A criterion for finite representation type, Math. Annalen269 (1984) 1–12.

    Google Scholar 

  14. Bongartz, K.: Indecomposables are standard, Comment. Math. Helv.60 (1985) 400–410.

    Google Scholar 

  15. Bongartz, K. and Gabriel, P.: Covering spaces in representation theory, Invent. Math.65 (1982) 331–378.

    Google Scholar 

  16. Bretscher, O. and Gabriel, P.: The standard form of a representation-finite algebra, Bull. Soc. Math. France111 (1983) 21–40.

    Google Scholar 

  17. Crawley-Boevey, W. W.: On tame algebras and bocses, Proc. London. Math. Soc.56 (1988) 451–483.

    Google Scholar 

  18. Dräxler, P.: Aufrichtige gerichtete Ausnahmealgebren, Bayreuter Math. Schriften29 (1989).

  19. Dräxler, P.: Sur les algèbres exceptionelles de Bongartz, C. R. Acad. Sci. Paris311 (1990) 495–498.

    Google Scholar 

  20. 20. Dräxler, P.: Completely separating algebras, J. Algebra165 (1994) 550–565.

    Google Scholar 

  21. Drozd, Yu A.: Tame and wild matrix problems, in: Representation Theory II, Lecture Notes in Math.832, Springer-Verlag (1980) 242–258.

    Google Scholar 

  22. Gabriel, P. and Roiter, A. V.: Representations of Finite-Dimensional Algebras, Algebra VIII, Encyclopedia Math. Sci.73, Springer-Verlag, 1992.

  23. Happel, D. and Vossieck, D.: Minimal algebras of infinite representation type with preprojective component, Manuscripta Math.42 (1983) 221–243.

    Google Scholar 

  24. Kerner, O.: Tilting wild algebras, J. London Math. Soc.39 (1989) 29–47.

    Google Scholar 

  25. Kerner, O. and Skowroński, A.: On module categories with nilpotent infinite radical, Compositio Math.77 (1991) 313–333.

    Google Scholar 

  26. Lersch, M.: Minimal wilde Algebren, Diplomarbeit(Düsseldorf 1987).

  27. Liu, S.: Semi-stable components of an Auslander-Reiten quiver, J. London Math. Soc.47 (1993) 405–416.

    Google Scholar 

  28. Liu, S.: Infinite radicals in standard Auslander-Reiten components, J. Algebra166 (1994) 245–254.

    Google Scholar 

  29. Nörenberg, R. and Skowroński, A.: Tame minimal non-polynomial growth simply connected algebras, Colloq. Math., in press.

  30. Peng, L. G. and Xiao, J.: On the number of DTr-orbits containing directing modules, Proc. Amer. Math. Soc.118 (1993) 753–756.

    Google Scholar 

  31. de la Peña, J. A.: On the representation type of one point extensions of tame concealed algebras, Manuscripta Math.61 (1988) 183–194.

    Google Scholar 

  32. de la Peña, J. A.: Algebras with hypercritical Tits form, in: Topics in Algebra, Banach Center Publ.26, Part 1 (PWN, Warsaw 1990) 353–369.

    Google Scholar 

  33. de la Peña, J. A.: Tame algebras with sincere directing modules, J. Algebra161 (1993) 171–185.

    Google Scholar 

  34. de la Peña, J. A.: The families of two-parametric tame algebras with sincere directing modules, in: Representations of Algebras, CMS Conf. Proc.14 (1993) 361–392.

    Google Scholar 

  35. de la Peña, J. A. and Skowroński, A.: Forbidden subalgebras of nonpolynomial growth tame simply connected algebras, Canadian J. Math.48 (1996) 1018–1043.

    Google Scholar 

  36. de la Peña, J.A. and Tamé, B.: Iterated tubular algebras, J. Pure Appl. Algebra64 (1990) 303–314.

    Google Scholar 

  37. Pogorzały, Z. and Skowroński, A.: On algebras whose indecomposable modules are multiplicity-free, Proc. London Math. Soc.47 (1983) 463–479.

    Google Scholar 

  38. Ringel, C. M.: Finite dimensional hereditary algebras of wild representation type, Math. Z.161 (1978) 236–255.

    Google Scholar 

  39. Ringel, C. M.: Tame algebras and integral quadratic forms, Lecture Notes in Math.1099 (Springer-Verlag 1984).

  40. Rogat, A. and Tesche, T.: The Gabriel quivers of the sincere simply connected algebras, Preprint 93-005, SFB 343 (Bielefeld).

  41. Simson, D.: Linear representations of partially ordered sets and vector space categories, Algebra, Logic and Applications Series4 (Gordon Breach Sci. Publ. 1992).

  42. Simson, D.: Kronecker triangles and non-polynomial growth, C. R. Acad. Sci. Paris, t. 321, Serie I (1995) 33–38.

    Google Scholar 

  43. Skowroński, A.: Algebras of polynomial growth, in: Topics in Algebra, Banach Center Publications, 26, Part 1 (PWN, Warsaw 1990) 535–568.

    Google Scholar 

  44. Skowroński, A.: Simply connected algebras and Hochschild cohomologies, in: Representations of Algebras, CMS Conf. Proc., 14 (1993) 431–447.

    Google Scholar 

  45. Skowroński, A.: Regular Auslander-Reiten components containing directing modules, Proc. Amer. Math. Soc. 120 (1994) 19–26.

    Google Scholar 

  46. Skowroński, A.: Cycles in module categories, in: Finite Dimensional Algebras and Related Topics, NATO ASI Series, Series C, Vol. 424, Kluwer Acad. Publ., Dortrecht 1994, pp. 309–345.

    Google Scholar 

  47. Skowroński, A.: Generalized standard Auslander-Reiten components, J. Math. Soc. Japan46 (1994) 517–543.

    Google Scholar 

  48. Skowroński, A.: On semi-regular Auslander-Reiten components, Bull. Polish Acad. Sci., Mathematics 42 (1994) 157–163.

    Google Scholar 

  49. Skowroński, A.: Criteria for polynomial growth of algebras, Bull. Polish Acad. Sci., Mathematics 42 (1994) 173–183.

    Google Scholar 

  50. Skowroński, A.: Cycle-finite algebras, J. Pure Appl. Algebra103 (1995) 105–116.

    Google Scholar 

  51. Skowroński, A.: Module categories over tame algebras, in: Representation Theory and Related Topics, Workshop Mexico 1994, CMS Conf. Proc.19 (1996) 281–313.

    Google Scholar 

  52. Skowroński, A.: Tame algebras with strongly simply connected Galois coverings, Colloq. Math.72 (1997) 335–351.

    Google Scholar 

  53. Skowroński, A. and Smalø, S. O.: Directing modules, J. Algebra147 (1992) 137–146.

    Google Scholar 

  54. Skowroński, A. and Waschbüsch, J.: Representation-finite biserial algebras, J. Reine Angew. Math.345 (1983) 172–181.

    Google Scholar 

  55. Unger, L.: The concealed algebras of the minimal wild, hereditary algebras, Bayreuter Math. Schriften31 (1990) 145–154.

    Google Scholar 

  56. Wittman, J.: Verkleidete zahme and minimal wilde Algebren, Diplomarbeit(Bayreuth 1990).

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

    ANDRZEJ SKOWROŃSKI

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SKOWROŃSKI, A. Simply connected algebras of polynomial growth. Compositio Mathematica 109, 99–133 (1997). https://doi.org/10.1023/A:1000245728528

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