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1999 | 82 | 1 | 85-103
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Additive functions for quivers with relations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Additive functions for quivers with relations extend the classical concept of additive functions for graphs. It is shown that the concept, recently introduced by T. Hübner in a special context, can be defined for different homological levels. The existence of such functions for level 2 resp. ∞ relates to a nonzero radical of the Tits resp. Euler form. We derive the existence of nonnegative additive functions from a family of stable tubes which stay tubes in the derived category, we investigate when this situation does appear and we study the restrictions imposed by the existence of a positive additive function.
Słowa kluczowe
Rocznik
Tom
82
Numer
1
Strony
85-103
Opis fizyczny
Daty
wydano
1999
otrzymano
1999-03-22
poprawiono
1999-05-06
Twórcy
  • Fachbereich Mathematik-Informatik, Universität-GH Paderborn, D-33095 Paderborn, Germany
autor
  • Department of Mathematical Sciences, Norwegian University of Science and Technology, N-7491 Trondheim, Norway
Bibliografia
  • [1] I. Assem and A. Skowroński, Algebras with cycle-finite derived categories, Math. Ann. 280 (1988), 441-463.
  • [2] M. Auslander, I. Reiten and S. O. Smalο, Representation Theory of Artin Algebras, Cambridge Univ. Press, 1995.
  • [3] H. S. M. Coxeter, Regular Polytopes, 3rd ed., Dover, 1973.
  • [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, U. Preiser and C. M. Ringel, Binary polyhedral groups and Euclidean diagrams, Manuscripta Math. 31 (1980), 317-329.
  • [7] D. Happel, I. Reiten and S. O. Smalο, Tilting in abelian categories and quasitilted algebras, Mem. Amer. Math. Soc. 575 (1996).
  • [8] D. Happel, J. Rickard and A. Schofield, Piecewise hereditary algebra, Bull. London Math. Soc. 20 (1988), 23-28.
  • [9] T. Hübner, Rank additivity for quasitilted algebras of canonical type, Colloq. Math. 75 (1998), 183-193.
  • [10] O. Kerner, Tilting wild algebras, J. London Math. Soc. 39 (1989), 29-47.
  • [11] 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), CMS Conf. Proc. 14, Amer. Math. Soc., 1993, 313-337.
  • [12] H. Lenzing and H. Meltzer, Tilting sheaves and concealed-canonical algebras, in: Representations of Algebras (Cocoyoc, 1994), CMS Conf. Proc. 18, Amer. Math. Soc., 1996, 455-473.
  • [13] H. Lenzing and J. A. de la Pe na, Concealed-canonical algebras and separating tubular families, Proc. London. Math. Soc. 78 (1999), 513-540.
  • [14] H. Lenzing and A. Skowroński, Quasi-tilted algebras of canonical type, Colloq. Math. 71 (1996), 161-181.
  • [15] H. Meltzer, Exceptional vector bundles, tilting sheaves and tilting complexes on weighted projective lines, Habilitationsschrift, TU Chemnitz, 1997.
  • [16] R. Nörenberg and A. Skowroński, Tame minimal non-polynomial growth strongly simply connected algebras, in: Representations of Algebras (Cocoyoc, 1994), CMS Conf. Proc. 18, Amer. Math. Soc., 1996, 519-538.
  • [17] I. Reiten, Dynkin diagrams and the representation theory of algebras, Notices Amer. Math. Soc. 44 (1997), 546-566.
  • [18] I. Reiten and A. Skowroński, Sincere stable tubes, preprint, 1999.
  • [19] C. M. Ringel, Tame Algebras and Integral Quadratic Forms, Lecture Notes in Math. 1099, Springer, 1984
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv82i1p85bwm
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