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

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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.
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  • Fachbereich Mathematik-Informatik, Universität-GH Paderborn, D-33095 Paderborn, Germany
  • Department of Mathematical Sciences, Norwegian University of Science and Technology, N-7491 Trondheim, Norway
  • [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
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