Trivial extensions of a certain subclass of minimal 2-fundamental algebras are examined. For such algebras the characterization of components of the Auslander-Reiten quiver which contain indecomposable projective modules is given.
@article{bwmeta1.element.doi-10_2478_s11533-007-0033-1, author = {Jaworska Alicja}, title = {On components of the Auslander-Reiten quiver of trivial extensions of 2-fundamental algebras which contain projective modules}, journal = {Open Mathematics}, volume = {5}, year = {2007}, pages = {665-685}, zbl = {1151.16019}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-007-0033-1} }
Jaworska Alicja. On components of the Auslander-Reiten quiver of trivial extensions of 2-fundamental algebras which contain projective modules. Open Mathematics, Tome 5 (2007) pp. 665-685. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-007-0033-1/
[1] I. Assem, D. Simson and A. Skowroński: Elements of the representation theory of associative algebras, Vol. 1, Techniques of representation theory, London Mathematical Society Student Texts, 65, Cambridge University Press, Cambridge, 2006. | Zbl 1092.16001
[2] M. Auslander and I. Reiten: “Uniserial functors”, Representation theory II, Proc. Second Internat. Conf., Carleton Univ., Ottawa, Ont., (1979), pp. 1–47, Lecture Notes in Math., 832, Springer, Berlin, 1980.
[3] M.C.R. Butler and C.M. Ringel: “Auslander-Reiten sequences with few middle terms and applications to string algebras”, Comm. Algebra, Vol. 15, (1987), no. 1–2, pp. 145–179. http://dx.doi.org/10.1080/00927878708823416 | Zbl 0612.16013
[4] P. Gabriel: “Auslander-Reiten sequences and representation-finite algebras”, Representation theory I, Proc. Workshop, Carleton Univ., Ottawa, Ont., (1979), pp. 1–71, Lecture Notes in Math., 831, Springer, Berlin, 1980.
[5] C. Geiss: “On components of type for string algebras”, Comm. Algebra, Vol. 26, (1998), no. 3, pp. 749–758. http://dx.doi.org/10.1080/00927879808826161
[6] A. Jaworska and Z. Pogorzały: “On trivial extensions of 2-fundamental algebras”, Comm. Algebra, Vol. 34, (2006), no. 11, pp. 3935–3947. http://dx.doi.org/10.1080/00927870600862748 | Zbl 1152.16017
[7] Z. Pogorzały and M. Sufranek: “Starting and ending components of the Auslander-Reiten quivers of a class of special biserial algebras”, Colloq. Math., Vol. 99, (2004), no. 1, pp. 111–144. | Zbl 1107.16022
[8] A. Skowroński: “Generalized standard Auslander-Reiten components”, J. Math. Soc. Japan, Vol. 46, (1994), no. 3, pp. 517–543. http://dx.doi.org/10.2969/jmsj/04630517 | Zbl 0828.16011
[9] A. Skowroński: Algebras of polynomial growth, Topics in algebra, Part 1 (Warsaw, 1988), pp. 535–568, Banach Center Publ., 26, Part 1, PWN, Warsaw, 1990.
[10] A. Skowroński and J. Waschbüsch: “Representation-finite biserial algebras”, J. Reine Angew. Math., Vol. 345, (1983), pp. 172–181. | Zbl 0511.16021