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1994-1995 | 146 | 3 | 251-266
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Iterated coil enlargements of algebras

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Let Λ be a finite-dimensional, basic and connected algebra over an algebraically closed field, and mod Λ be the category of finitely generated right Λ-modules. We say that Λ has acceptable projectives if the indecomposable projective Λ-modules lie either in a preprojective component without injective modules or in a standard coil, and the standard coils containing projectives are ordered. We prove that for such an algebra Λ the following conditions are equivalent: (a) Λ is tame, (b) the Tits form $q_Λ$ of Λ is weakly non-negative, (c)~Λ is an iterated coil enlargement
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  • [1] I. Assem and A. Skowroński, Minimal representation-infinite coil algebras, Manuscripta Math. 67 (1990), 305-331.
  • [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: Proc. ICRA VI (Ottawa, 1992), Canad. Math. Soc. Conf. Proc. 14, 1993, 29-68.
  • [4] I. Assem, A. Skowroński and B. Tomé, Coil enlargements of algebras, Tsukuba J. Math., to appear.
  • [5] M. Auslander and S. O. Smalø, Almost split sequences in subcategories, J. Algebra 69 (1981), 426-454.
  • [6] K. Bongartz, Algebras and quadratic forms, J. London Math. Soc. 28 (1983), 461-469.
  • [7] K. Bongartz and P. Gabriel, Covering spaces in representation theory, Invent. Math. 65 (1981), 331-378.
  • [8] Yu. Drozd, Tame and wild matrix problems, in: Proc. ICRA II (Ottawa, 1979), Lecture Notes in Math. 832, Springer, Berlin, 1980, 240-258.
  • [9] J. A. de la Pe na, On the representation type of one-point extensions of tame concealed algebras, Manuscripta Math. 61 (1988), 183-194.
  • [10] J. A. de la Pe na and B. Tomé, Iterated tubular algebras, J. Pure Appl. Algebra 64 (1990), 303-314.
  • [11] C. M. Ringel, Tame Algebras and Integral Quadratic Forms, Lecture Notes in Math. 1099, Springer, Berlin, 1984.
  • [12] A. Skowroński, Algebras of polynomial growth, in: Topics in Algebra, Banach Center Publ. 26, Part I, PWN, Warszawa, 1990, 535-568.
  • [13] A. Skowroński, Tame algebras with simply connected Galois coverings, in preparation.
  • [14] A. Skowroński, Cycle-finite algebras, J. Pure Appl. Algebra, to appear.
  • [15] A. Skowroński, Cycles in module categories, in: Proc. Canad. Math. Soc. Annual Seminar-NATO Advanced Research Workshop on Representations of Algebras and Related Topics (Ottawa 1992).
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bwmeta1.element.bwnjournal-article-fmv146i3p251bwm
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