On a family of vector space categories

Grzegorz Bobiński; Andrzej Skowroński

Open Mathematics (2003)

  • Volume: 1, Issue: 3, page 332-359
  • ISSN: 2391-5455

Abstract

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In continuation of our earlier work [2] we describe the indecomposable representations and the Auslander-Reiten quivers of a family of vector space categories playing an important role in the study of domestic finite dimensional algebras over an algebraically closed field. The main results of the paper are applied in our paper [3] where we exhibit a wide class of almost sincere domestic simply connected algebras of arbitrary large finite global dimensions and describe their Auslander-Reiten quivers.

How to cite

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Grzegorz Bobiński, and Andrzej Skowroński. "On a family of vector space categories." Open Mathematics 1.3 (2003): 332-359. <http://eudml.org/doc/268828>.

@article{GrzegorzBobiński2003,
abstract = {In continuation of our earlier work [2] we describe the indecomposable representations and the Auslander-Reiten quivers of a family of vector space categories playing an important role in the study of domestic finite dimensional algebras over an algebraically closed field. The main results of the paper are applied in our paper [3] where we exhibit a wide class of almost sincere domestic simply connected algebras of arbitrary large finite global dimensions and describe their Auslander-Reiten quivers.},
author = {Grzegorz Bobiński, Andrzej Skowroński},
journal = {Open Mathematics},
keywords = {16G20; 16G60; 16G70},
language = {eng},
number = {3},
pages = {332-359},
title = {On a family of vector space categories},
url = {http://eudml.org/doc/268828},
volume = {1},
year = {2003},
}

TY - JOUR
AU - Grzegorz Bobiński
AU - Andrzej Skowroński
TI - On a family of vector space categories
JO - Open Mathematics
PY - 2003
VL - 1
IS - 3
SP - 332
EP - 359
AB - In continuation of our earlier work [2] we describe the indecomposable representations and the Auslander-Reiten quivers of a family of vector space categories playing an important role in the study of domestic finite dimensional algebras over an algebraically closed field. The main results of the paper are applied in our paper [3] where we exhibit a wide class of almost sincere domestic simply connected algebras of arbitrary large finite global dimensions and describe their Auslander-Reiten quivers.
LA - eng
KW - 16G20; 16G60; 16G70
UR - http://eudml.org/doc/268828
ER -

References

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  1. [1] M. Auslander, I. Reiten, S. Smalø: Representation theory of Artin algebras, Cambridge Studies in Advanced Mathematics 36, Cambridge University Press, Cambridge, 1995. Zbl0834.16001
  2. [2] G. Bobiński, P. Dräxler, A. Skowroński: “Domestic algebras with many nonperiodic Auslander-Reiten components”, Comm. Algebra, Vol. 31 (2003), pp. 1881–1926. http://dx.doi.org/10.1081/AGB-120018513 Zbl1062.16026
  3. [3] G. Bobiński and A. Skowroński: Domestic iterated one-point extensions of algebras by two-ray modules, preprint, Toruń, 2002. Zbl1061.16021
  4. [4] C.M. Ringel: “Tame algebras”, In: Representation Theory I, Lecture Notes in Math. 831, Springer-Verlag, Berlin-New York, 1980, pp. 134–287. 
  5. [5] C.M. Ringel: Tame Algebras and Integral Quadratic Forms, Lecture Notes in Math. 1099, Springer-Verlag, Berlin-New York, 1984. 
  6. [6] D. Simson: Linear Representations of Partially Ordered Sets and Vector Space Categories, Algebra, Logic and Appl. 4, Gordon and Breach, Montreux, 1992. 

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