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2000 | 86 | 1 | 137-152
Tytuł artykułu

On the K-theory of tubular algebras

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Języki publikacji
EN
Abstrakty
EN
Let Λ be a tubular algebra over an arbitrary base field. We study the Grothendieck group $K_{0}(Λ)$, endowed with the Euler form, and its automorphism group $Aut(K_{0}(Λ))$ on a purely K-theoretical level as in [7]. Our results serve as tools for classifying the separating tubular families of tubular algebras as in the example [5] and for determining the automorphism group $Aut(D^{b}Λ)$ of the derived category of Λ.
Słowa kluczowe
Rocznik
Tom
86
Numer
1
Strony
137-152
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-08-02
poprawiono
1999-11-10
Twórcy
autor
  • Fachbereich 17 Mathematik, Universität Paderborn, D-33095 Paderborn, Germany
Bibliografia
  • [1] M. Barot, Representation-finite derived tubular algebras, Arch. Math. (Basel) 74 (2000), 83-94.
  • [2] M. Barot and J. A. de la Pe na, Derived tubular strongly simply connected algebras, Proc. Amer. Math. Soc. 127 (1999), 647-655.
  • [3] D. Happel, Triangulated Categories in the Representation Theory of Finite Dimensional Algebras, London Math. Soc. Lecture Note Ser. 119, Cambridge Univ. Press, 1988.
  • [4] N. Koblitz, Introduction to Elliptic Curves and Modular Forms, Grad. Texts in Math., 97, Springer, Berlin, 1984.
  • [5] D. Kussin, Non-isomorphic derived-equivalent tubular curves and their associated tubular algebras, J. Algebra 226 (2000), 436-450.
  • [6] D. Kussin, Graduierte Faktorialität und die Parameterkurven tubularer Familien, Ph.D. thesis, Universität Paderborn, 1997.
  • [7] H. Lenzing, A K-theoretic study of canonical algebras, in: Representation Theory of Algebras (Cocoyoc, 1994), R. Bautista, R. Mart\'\inez-Villa, and J. A. de la Pe na (eds.), CMS Conf. Proc. 18, Amer. Math. Soc., Providence, RI, 1996, 433-473.
  • [8] H. Lenzing, Representations of finite dimensional algebras and singularity theory, in: Trends in Ring Theory (Miskolc, 1996) V. Dlab et al. (eds.), CMS Conf. Proc. 22, Amer. Math. Soc., Providence, RI, 1998, 71-97.
  • [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 H. Meltzer, Sheaves on a weighted projective line of genus one, and representations of a tubular algebra, in: Representations of Algebras (Ottawa 1992), V. Dlab and H. Lenzing (eds.), CMS Conf. Proc. 14, Amer. Math. Soc., Providence, RI, 1993, 313-337.
  • [11] H. Lenzing and J. A. de la Pe na, Concealed-canonical algebras and separating tubular families, Proc. London Math. Soc. 78 (1999), 513-540.
  • [12] C. M. Ringel, Tame Algebras and Integral Quadratic Forms, Lecture Notes in Math. 1099, Springer, Berlin, 1984.
  • [13] C. M. Ringel, The canonical algebras, in: Topics in Algebra, Banach Center Publ. 26, 1990, with an appendix by William Crawley-Boevey, 407-432.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-cmv86i1p137bwm
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