On a family of vector space categories

• Autorzy: Grzegorz Bobiński , Andrzej Skowroński
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

vector space category; subspace category; domestic type; Auslander-Reiten quiver; algebra; one-point extension; 16G20; 16G60; 16G70

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2003
• Tom: 1
• Numer: 3
• Strony: 332-359

Daty

wydano

2003-09-01

online

2003-09-01

Twórcy

autor

Grzegorz Bobiński

• Nicolaus Copernicus University

autor

Andrzej Skowroński

• Nicolaus Copernicus University

Bibliografia

• [1] M. Auslander, I. Reiten, S. Smalø: Representation theory of Artin algebras, Cambridge Studies in Advanced Mathematics 36, Cambridge University Press, Cambridge, 1995.
• [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
• [3] G. Bobiński and A. Skowroński: Domestic iterated one-point extensions of algebras by two-ray modules, preprint, Toruń, 2002.
• [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.

Identyfikatory

DOI

10.2478/BF02475214