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.
@article{bwmeta1.element.doi-10_2478_BF02475214,
author = {Grzegorz Bobi\'nski and Andrzej Skowro\'nski},
title = {On a family of vector space categories},
journal = {Open Mathematics},
volume = {1},
year = {2003},
pages = {332-359},
zbl = {1050.16007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02475214}
}
Grzegorz Bobiński; Andrzej Skowroński. On a family of vector space categories. Open Mathematics, Tome 1 (2003) pp. 332-359. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02475214/
[1] M. Auslander, I. Reiten, S. Smalø: Representation theory of Artin algebras, Cambridge Studies in Advanced Mathematics 36, Cambridge University Press, Cambridge, 1995. | Zbl 0834.16001
[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 | Zbl 1062.16026
[3] G. Bobiński and A. Skowroński: Domestic iterated one-point extensions of algebras by two-ray modules, preprint, Toruń, 2002. | Zbl 1061.16021
[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] C.M. Ringel: Tame Algebras and Integral Quadratic Forms, Lecture Notes in Math. 1099, Springer-Verlag, Berlin-New York, 1984.
[6] D. Simson: Linear Representations of Partially Ordered Sets and Vector Space Categories, Algebra, Logic and Appl. 4, Gordon and Breach, Montreux, 1992.