Skip to content
BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access September 1, 2003

On a family of vector space categories

Grzegorz Bobiński and Andrzej Skowroński
From the journal Open Mathematics

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: 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. 10.1017/CBO9780511623608Search in 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-12001851310.1081/AGB-120018513Search in Google Scholar

[3] G. Bobiński and A. Skowroński: Domestic iterated one-point extensions of algebras by two-ray modules, preprint, Toruń, 2002. 10.2478/BF02475179Search in 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. Search in Google Scholar

[5] C.M. Ringel: Tame Algebras and Integral Quadratic Forms, Lecture Notes in Math. 1099, Springer-Verlag, Berlin-New York, 1984. 10.1007/BFb0072870Search in 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. Search in Google Scholar

Published Online: 2003-9-1
Published in Print: 2003-9-1

© 2003 Versita Warsaw

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Scroll Up Arrow