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2004 | 2 | 1 | 19-49
Tytuł artykułu

Classification of discrete derived categories

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Języki publikacji
EN
Abstrakty
EN
The main aim of the paper is to classify the discrete derived categories of bounded complexes of modules over finite dimensional algebras.
Wydawca
Czasopismo
Rocznik
Tom
2
Numer
1
Strony
19-49
Opis fizyczny
Daty
wydano
2004-03-01
online
2004-03-01
Twórcy
Bibliografia
  • [1] I. Assem and D. Happel: “Generalized tilted algebras of type \(\mathbb{A}_n \) ”, Comm. Algebra, Vol. 9, (1981), pp. 2101–2125.
  • [2] I. Assem and A. Skowroński: “Iterated tilted algebras of type \( \tilde{\mathbb{A}}_n\) ”, Math. Z., Vol. 195, (1987), pp. 269–290. http://dx.doi.org/10.1007/BF01166463
  • [3] I. Assem and A. Skowroński: “Algebras with cycle-finite derived categories”, Math. Ann., Vol. 280, (1988), pp. 441–463. http://dx.doi.org/10.1007/BF01456336
  • [4] M. Auslander, M. Platzeck and I. Reiten: “Coxeter functors without diagrams”, Trans. Amer. Math. Soc., Vol. 250, (1979), pp. 1–46. http://dx.doi.org/10.2307/1998978
  • [5] M. Barot and J. A. de la Peña: “The Dynkin type of non-negative unit form”, Expo. Math., Vol. 17, (1999), pp. 339–348.
  • [6] K. Bongartz: “Tilted Algebras”, Lecture Notes in Math., Vol. 903, (1981), pp. 26–38.
  • [7] K. Bongartz and P. Gabriel: “Covering spaces in representation theory”, Invent. Math., Vol. 65, (1981), pp. 331–378. http://dx.doi.org/10.1007/BF01396624
  • [8] M. C. R. Butler and C. M. Ringel: “Auslander-Reiten sequences with few middle terms and applications to string algebras”, Comm. Algebra, Vol. 15, (1987), pp. 145–179.
  • [9] Ch. Geiß and J. A. de la Peña: “Auslander-Reiten components for clans”, Bol. Soc. Mat. Mexicana, Vol. 5, (1999), pp. 307–326.
  • [10] D. Happel: Triangulated categories in the representation theory of finite-dimensional algebras, London Math. Soc. Lecture Note Series, 1988.
  • [11] D. Happel: “Auslander-Reiten triangles in derived categories of finite-dimensional algebras”, Proc. Amer. Math. Soc., Vol. 112, (1991), pp. 641–648. http://dx.doi.org/10.2307/2048684
  • [12] D. Happel and C. M. Ringel: “Tilted algebras”, Trans. Amer. Math. Soc., Vol. 274, (1982), pp. 399–443. http://dx.doi.org/10.2307/1999116
  • [13] D. Hughes and J. Waschbüsch: “Trivial extensions of tilted algebras”, Proc. London Math. Soc., Vol. 46, (1983), pp. 347–364.
  • [14] B. Keller and D. Vossieck: “Aisles in derived, categories”, Bull. Soc. Math. Belg., Vol. 40, (1988), pp. 239–253.
  • [15] J. Nehring: “Polynomial growth trivial extensions of non-simply connected algebras”, Bull. Polish Acad. Sci. Math., Vol. 36, (1988), pp. 441–445.
  • [16] J. Rickard: “Morita theory for derived categories”, J. London Math. Soc., Vol. 39, (1989), pp. 436–456.
  • [17] C. M. Ringel: Tame Algebras and Integral Quadratic Forms, Lecture Notes in Math., 1984.
  • [18] C. M. Ringel: “The repetitive algebra of a gentle algebra”, Bol. Soc. Mat. Mexicana, Vol. 3, (1997), pp. 235–253.
  • [19] A. Skowroński and J. Waschbüsch: “Representation-finite biserial algebras”, J. Reine Angew. Math., Vol. 345, (1983), pp. 172–181.
  • [20] J. L. Verdier: “Categories derivées, état 0”, Lecture Notes in Math., Vol. 569, (1977), pp. 262–331.
  • [21] D. Vossieck: “The algebras with discrete derived category”, J. Algebra, Vol. 243, (2001), pp. 168–176. http://dx.doi.org/10.1006/jabr.2001.8783
  • [22] H. Tachikawa and T. Wakamatsu: “Applications of reflection functors for selfinjective algebras”, Lecture Notes in Math., Vol. 1177, (1986), pp. 308–327. http://dx.doi.org/10.1007/BFb0075271
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.doi-10_2478_BF02475948
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