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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Vespri, Vincenzo / Marano, Salvatore Angelo


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Online
ISSN
2391-5455
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Volume 1, Issue 3

Issues

Volume 13 (2015)

On a family of vector space categories

Grzegorz Bobiński / Andrzej Skowroński
Published Online: 2003-09-01 | DOI: https://doi.org/10.2478/BF02475214

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.

Keywords: vector space category; subspace category; domestic type; Auslander-Reiten quiver; algebra; one-point extension

Keywords: 16G20; 16G60; 16G70

  • [1] M. Auslander, I. Reiten, S. Smalø: Representation theory of Artin algebras, Cambridge Studies in Advanced Mathematics 36, Cambridge University Press, Cambridge, 1995. Google Scholar

  • [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-120018513CrossrefGoogle Scholar

  • [3] G. Bobiński and A. Skowroński: Domestic iterated one-point extensions of algebras by two-ray modules, preprint, Toruń, 2002. Google Scholar

  • [4] C.M. Ringel: “Tame algebras”, In: Representation Theory I, Lecture Notes in Math. 831, Springer-Verlag, Berlin-New York, 1980, pp. 134–287. Google Scholar

  • [5] C.M. Ringel: Tame Algebras and Integral Quadratic Forms, Lecture Notes in Math. 1099, Springer-Verlag, Berlin-New York, 1984. Google Scholar

  • [6] D. Simson: Linear Representations of Partially Ordered Sets and Vector Space Categories, Algebra, Logic and Appl. 4, Gordon and Breach, Montreux, 1992. Google Scholar

About the article

Published Online: 2003-09-01

Published in Print: 2003-09-01


Citation Information: Open Mathematics, Volume 1, Issue 3, Pages 332–359, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/BF02475214.

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© 2003 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

Citing Articles

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[1]
Grzegorz Bobiński
Communications in Algebra, 2006, Volume 34, Number 6, Page 2219
[2]
Grzegorz Bobiński
Acta Mathematica Sinica, English Series, 2007, Volume 23, Number 6, Page 1033
[3]
Grzegorz Bobiński and Andrzej Skowroński
Central European Journal of Mathematics, 2003, Volume 1, Number 4, Page 457

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