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2007 | 5 | 2 | 215-263
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On Hom-spaces of tame algebras

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Let Λ be a finite dimensional algebra over an algebraically closed field k and Λ has tame representation type. In this paper, the structure of Hom-spaces of all pairs of indecomposable Λ-modules having dimension smaller than or equal to a fixed natural number is described, and their dimensions are calculated in terms of a finite number of finitely generated Λ-modules and generic Λ-modules. In particular, such spaces are essentially controlled by those of the corresponding generic modules.
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Bibliografia
  • [1] R. Bautista: “The category of morphisms between projective modules” Comm. Algebra, Vol. 32(11), (2004), pp. 4303–4331. http://dx.doi.org/10.1081/AGB-200034145
  • [2] R. Bautista and Y. Zhang: “Representations of a k-algebra over the rational functions over k” J. Algebra, Vol.(267), (2003), pp. 342–358. http://dx.doi.org/10.1016/S0021-8693(03)00371-5
  • [3] R. Bautista, J. Boza and E. Pérez: “Reduction Functors and Exact Structures for Bocses” Bol. Soc. Mat. Mexicana, Vol. 9(3), (2003), pp. 21–60.
  • [4] P. Dräxler, I. Reiten, S. O. Smalø, O. Solberg and with an appendix by B. Keller: “Exact Categories and Vector Space Categories” Trans. A.M.S., Vol. 351(2), (1999), pp. 647–682. http://dx.doi.org/10.1090/S0002-9947-99-02322-3
  • [5] W.W. Crawley-Boevey: “On tame algebras and bocses” Proc. London Math. Soc., Vol.56, (1988), pp. 451–483. http://dx.doi.org/10.1112/plms/s3-56.3.451
  • [6] W.W. Crawley-Boevey: “Tame algebras and generic modules” Proc. London Math. Soc., Vol. 63, (1991), pp. 241–265. http://dx.doi.org/10.1112/plms/s3-63.2.241
  • [7] Yu.A. Drozd: “Tame and wild matrix problems” Amer. Math. Soc. Transl., Vol. 128(2), (1986), pp 31–55.
  • [8] Yu.A. Drozd: “Reduction algorithm and representations of boxes and algebras” C.R. Math. Acad. Sci. Soc. R. Can., Vol. 23(4), (2001), pp. 91–125.
  • [9] P. Gabriel and A.V. Roiter: “Representations of finite-dimensional algebras” In: A.I. Kostrikin and I.V. Shafarevich (Eds.): Encyclopaedia of the Mathematical Sciences, Vol.(73), Algebra VIII, Springer, 1992.
  • [10] X. Zeng and Y. Zhang: “A correspondence of almost split sequences between some categories” Comm. Algebra, Vol. 29(2), (2001), pp. 557–582. http://dx.doi.org/10.1081/AGB-100001524
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bwmeta1.element.doi-10_2478_s11533-007-0002-8
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