On Hom-spaces of tame algebras

Raymundo Bautista; Yuriy Drozd; Xiangyong Zeng; Yingbo Zhang

Open Mathematics (2007)

  • Volume: 5, Issue: 2, page 215-263
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Raymundo Bautista, et al. "On Hom-spaces of tame algebras." Open Mathematics 5.2 (2007): 215-263. <http://eudml.org/doc/269417>.

@article{RaymundoBautista2007,
abstract = {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.},
author = {Raymundo Bautista, Yuriy Drozd, Xiangyong Zeng, Yingbo Zhang},
journal = {Open Mathematics},
keywords = {Generic module; infinite radical; bocs; finite-dimensional algebras; tame representation type; generic modules; bocses; indecomposable modules},
language = {eng},
number = {2},
pages = {215-263},
title = {On Hom-spaces of tame algebras},
url = {http://eudml.org/doc/269417},
volume = {5},
year = {2007},
}

TY - JOUR
AU - Raymundo Bautista
AU - Yuriy Drozd
AU - Xiangyong Zeng
AU - Yingbo Zhang
TI - On Hom-spaces of tame algebras
JO - Open Mathematics
PY - 2007
VL - 5
IS - 2
SP - 215
EP - 263
AB - 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.
LA - eng
KW - Generic module; infinite radical; bocs; finite-dimensional algebras; tame representation type; generic modules; bocses; indecomposable modules
UR - http://eudml.org/doc/269417
ER -

References

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  1. [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 Zbl1081.16025
  2. [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 Zbl1029.16009
  3. [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. Zbl1067.16011
  4. [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 Zbl0916.16002
  5. [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 Zbl0661.16026
  6. [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 Zbl0741.16005
  7. [7] Yu.A. Drozd: “Tame and wild matrix problems” Amer. Math. Soc. Transl., Vol. 128(2), (1986), pp 31–55. Zbl0583.16022
  8. [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. Zbl1031.16010
  9. [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. [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 Zbl1034.16023

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