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2000 | 86 | 2 | 209-230
Tytuł artykułu

Roots of Nakayama and Auslander-Reiten translations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We discuss the roots of the Nakayama and Auslander-Reiten translations in the derived category of coherent sheaves over a weighted projective line. As an application we derive some new results on the structure of selfinjective algebras of canonical type.
Słowa kluczowe
Rocznik
Tom
86
Numer
2
Strony
209-230
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-07-27
poprawiono
2000-01-20
Twórcy
  • Fachbereich Mathematik-Informatik, Universität-GH Paderborn, D-33095 Paderborn, Germany
  • Faculty of Mathematics and Informatics, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland
Bibliografia
  • [1] I. Assem, J. Nehring and A. Skowroński, Domestic trivial extensions of simply connected algebras, Tsukuba J. Math. 13 (1989), 31-72.
  • [2] K. Bongartz, Critical simply connected algebras, Manuscripta Math. 46 (1984), 117-136.
  • [3] H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 3rd ed., Springer, 1972.
  • [4] W. Geigle and H. Lenzing, A class of weighted projective curves arising in representation theory of finite dimensional algebras, in: Singularities, Representations of Algebras, and Vector Bundles, Lecture Notes in Math. 1273, Springer, 1987, 265-297.
  • [5] D. Happel, Triangulated Categories in the Representation Theory of Finite Dimensional Algebras, London Math. Soc. Lecture Note Ser. 119, Cambridge Univ. Press, 1988.
  • [6] D. Happel and D. Vossieck, Minimal algebras of infinite representation type with preprojective component, Manuscripta Math. 42 (1983), 221-243.
  • [7] D. Hughes and J. Waschbüsch, Trivial extensions of tilted algebras, Proc. London Math. Soc. 46 (1983), 347-364.
  • [8] H. Lenzing and H. Meltzer, Sheaves on a weighted projective line of genus one and representations of tubular algebras, in: Representations of Algebras, CMS Conf. Proc. 14, Amer. Math. Soc., 1993, 313-337.
  • [9] H. Lenzing and H. Meltzer, The automorphism group of the derived category for a weighted projective line, Comm. Algebra 28 (2000), 1685-1700.
  • [10] H. Lenzing and A. Skowroński, On selfinjective algebras of Euclidean type, Colloq. Math. 79 (1999), 71-76.
  • [11] H. Lenzing and A. Skowroński, Selfinjective algebras of wild canonical type, preprint, 1999.
  • [12] J. Nehring and A. Skowroński, Polynomial growth trivial extensions of simply connected algebras, Fund. Math. 132 (1989), 117-134.
  • [13] Y. Ohnuki, K. Takeda and K. Yamagata, Automorphisms of repetitive algebras, J. Algebra, to appear.
  • [14] C. M. Ringel, Tame Algebras and Integral Quadratic Forms, Lecture Notes in Math. 1099, Springer, 1984.
  • [15] A. Skowroński, Selfinjective algebras of polynomial growth, Math. Ann. 285 (1989), 177-199.
  • [16] A. Skowroński and K. Yamagata, Socle deformations of selfinjective algebras, Proc. London Math. Soc. 72 (1996), 545-566.
  • [17] A. Skowroński and K. Yamagata, Galois coverings of selfinjective algebras by repetitive algebras, Trans. Amer. Math. Soc. 351 (1999), 715-734.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv86i2p209bwm
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