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1996 | 149 | 1 | 67-82
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On Auslander–Reiten components for quasitilted algebras

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EN
Abstrakty
EN
An artin algebra A over a commutative artin ring R is called quasitilted if gl.dim A ≤ 2 and for each indecomposable finitely generated A-module M we have pd M ≤ 1 or id M ≤ 1. In [11] several characterizations of quasitilted algebras were proven. We investigate the structure and homological properties of connected components in the Auslander-Reiten quiver $Γ_A$ of a quasitilted algebra A.
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Twórcy
  • Department of Mathematics - IME, University of São Paulo, CP 20570, Cep 01452-990 Brasil, fucoelho@ime.usp.br
  • Faculty of Mathematics and Informatics, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland, skowron@mat.uni.torun.pl
Bibliografia
  • [1] I. Assem and F. U. Coelho, Glueings of tilted algebras, J. Pure Appl. Algebra 96 (1994), 225-243.
  • [2] M. Auslander and I. Reiten, Representation theory of artin algebras V, Comm. Algebra 5 (1977), 519-554.
  • [3] M. Auslander, I. Reiten and S. Smalø, Representation Theory of Artin Algebras, Cambridge Stud. Adv. Math. 36, Cambridge Univ. Press, 1995.
  • [4] R. Bautista and S. Smalø, Non-existent cycles, Comm. Algebra 11 (1983), 1755-1767.
  • [5] F. U. Coelho, Components of Auslander-Reiten quivers containing only preprojective modules, J. Algebra 157 (1993), 472-488.
  • [6] F. U. Coelho, A note on preinjective partial tilting modules, in: Representations of Algebras, CMS Conf. Proc. 14, Amer. Math. Soc., 1994, 109-115.
  • [7] F. U. Coelho, E. N. Marcos, H. A. Merklen and A. Skowroński, Domestic semiregular branch enlargements of tame concealed algebras, in: Representations of Algebras, ICRA VII, Cocoyoc (Mexico) 1994, CMS Conf. Proc., in press.
  • [8] V. Dlab and C. M. Ringel, Indecomposable representations of graphs and algebras, Mem. Amer. Math. Soc. 173 (1976).
  • [9] D. Happel, U. Preiser and C. M. Ringel, Vinberg's characterisation of Dynkin diagrams using subadditive functions with applications to DTr-periodic modules, in: Representation Theory II, Lecture Notes in Math. 832, Springer, 1980, 280-294.
  • [10] D. Happel and C. M. Ringel, Tilted algebras, Trans. Amer. Math. Soc. 274 (1982), 399-443.
  • [11] D. Happel, I. Reiten and S. Smalø, Tilting in abelian categories and quasitilted algebras, Mem. Amer. Math. Soc., in press.
  • [12] O. Kerner, Tilting wild algebras, J. London Math. Soc. 39 (1989), 29-47.
  • [13] O. Kerner, Stable components of wild tilted algebra, J. Algebra 142 (1991), 37-57.
  • [14] H. Lenzing and J. A. de la Pe na, Wild canonical algebras, Math. Z., in press.
  • [15] H. Lenzing and J. A. de la Pe na, Algebras with a separating tubular family, preprint, 1995.
  • [16] S. Liu, Semi-stable components of an Auslander-Reiten quiver, J. London Math. Soc. 47 (1993), 405-416.
  • [17] S. Liu, The connected components of the Auslander-Reiten quiver of a tilted algebra, J. Algebra 161 (1993), 505-523.
  • [18] C. M. Ringel, Finite dimensional hereditary algebras of wild representation type, Math. Z. 161 (1978), 235-255.
  • [19] C. M. Ringel, Tame Algebras and Integral Quadratic Forms, Lecture Notes in Math. 1099, Springer, 1984.
  • [20] C. M. Ringel, The regular components of the Auslander-Reiten quiver of a tilted algebra, Chinese Ann. Math. 9B (1988), 1-18.
  • [21] C. M. Ringel, The canonical algebras, in: Topics in Algebra, Banach Center Publ. 26, Part I, PWN, Warszawa, 1990, 407-432.
  • [22] A. Skowroński, Regular Auslander-Reiten components containing directing modules, Proc. Amer. Math. Soc. 120 (1994), 19-26.
  • [23] A. Skowroński, Minimal representation-infinite artin algebras, Math. Proc. Cambridge Philos. Soc. 116 (1994), 229-243.
  • [24] A. Skowroński, Cycle-finite algebras, J. Pure Appl. Algebra 103 (1995), 105-116.
  • [25] A. Skowroński, On omnipresent tubular families of modules, in: Representations of Algebras, ICRA, Cocoyoc (Mexico) 1994, CMS Conf. Proc., in press.
  • [26] A. Skowroński, Module categories with finite short cycles, in preparation.
  • [27] H. Strauss, On the perpendicular category of a partial tilting module, J. Algebra 144 (1991), 43-66.
  • [28] Y. Zhang, The structure of stable components, Canad. J. Math. 43 (1991), 652-672.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-fmv149i1p67bwm
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