On components of the Auslander-Reiten quiver of trivial extensions of 2-fundamental algebras which contain projective modules

Jaworska Alicja

Open Mathematics (2007)

  • Volume: 5, Issue: 4, page 665-685
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Jaworska Alicja. "On components of the Auslander-Reiten quiver of trivial extensions of 2-fundamental algebras which contain projective modules." Open Mathematics 5.4 (2007): 665-685. <http://eudml.org/doc/269177>.

@article{JaworskaAlicja2007,
abstract = {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.},
author = {Jaworska Alicja},
journal = {Open Mathematics},
keywords = {Trivial extension; Minimal 2-fundamental algebra; Auslander-Reiten quiver; Generalized standard components; trivial extensions; Auslander-Reiten quivers; generalized standard components; minimal 2-fundamental algebras; components},
language = {eng},
number = {4},
pages = {665-685},
title = {On components of the Auslander-Reiten quiver of trivial extensions of 2-fundamental algebras which contain projective modules},
url = {http://eudml.org/doc/269177},
volume = {5},
year = {2007},
}

TY - JOUR
AU - Jaworska Alicja
TI - On components of the Auslander-Reiten quiver of trivial extensions of 2-fundamental algebras which contain projective modules
JO - Open Mathematics
PY - 2007
VL - 5
IS - 4
SP - 665
EP - 685
AB - 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.
LA - eng
KW - Trivial extension; Minimal 2-fundamental algebra; Auslander-Reiten quiver; Generalized standard components; trivial extensions; Auslander-Reiten quivers; generalized standard components; minimal 2-fundamental algebras; components
UR - http://eudml.org/doc/269177
ER -

References

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  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. Zbl1092.16001
  2. [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. [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 Zbl0612.16013
  4. [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. [5] C. Geiss: “On components of type ℤ 𝔸 ∞ ∞ for string algebras”, Comm. Algebra, Vol. 26, (1998), no. 3, pp. 749–758. http://dx.doi.org/10.1080/00927879808826161 
  6. [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 Zbl1152.16017
  7. [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. Zbl1107.16022
  8. [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 Zbl0828.16011
  9. [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. [10] A. Skowroński and J. Waschbüsch: “Representation-finite biserial algebras”, J. Reine Angew. Math., Vol. 345, (1983), pp. 172–181. Zbl0511.16021

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