# 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

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topRaymundo 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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- [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] Yu.A. Drozd: “Tame and wild matrix problems” Amer. Math. Soc. Transl., Vol. 128(2), (1986), pp 31–55. Zbl0583.16022
- [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] 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 Zbl1034.16023

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