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2007 | 5 | 2 | 215-263
Tytuł artykułu

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.
Słowa kluczowe
  • UNAM, Unidad Morelia
  • Kyiv Taras Shevchenko University
  • Beijing Normal University
  • Beijing Normal University
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  • [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.
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  • [6] W.W. Crawley-Boevey: “Tame algebras and generic modules” Proc. London Math. Soc., Vol. 63, (1991), pp. 241–265.
  • [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.
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