Slice modules over minimal 2-fundamental algebras

Zygmunt Pogorzały; Karolina Szmyt

Open Mathematics (2007)

  • Volume: 5, Issue: 1, page 164-180
  • ISSN: 2391-5455

Abstract

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We consider a class of algebras whose Auslander-Reiten quivers have starting components that are not generalized standard. For these components we introduce a generalization of a slice and show that only in finitely many cases (up to isomorphism) a slice module is a tilting module.

How to cite

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Zygmunt Pogorzały, and Karolina Szmyt. "Slice modules over minimal 2-fundamental algebras." Open Mathematics 5.1 (2007): 164-180. <http://eudml.org/doc/269709>.

@article{ZygmuntPogorzały2007,
abstract = {We consider a class of algebras whose Auslander-Reiten quivers have starting components that are not generalized standard. For these components we introduce a generalization of a slice and show that only in finitely many cases (up to isomorphism) a slice module is a tilting module.},
author = {Zygmunt Pogorzały, Karolina Szmyt},
journal = {Open Mathematics},
keywords = {Minimal 2-fundamental algebra; Auslander-Reiten quiver; slice module; tilting module; minimal 2-fundamental algebras; Auslander-Reiten quivers; tilting modules; Auslander-Reiten components; postprojective slice modules; cotilting modules; hereditary algebras; preinjective slice modules},
language = {eng},
number = {1},
pages = {164-180},
title = {Slice modules over minimal 2-fundamental algebras},
url = {http://eudml.org/doc/269709},
volume = {5},
year = {2007},
}

TY - JOUR
AU - Zygmunt Pogorzały
AU - Karolina Szmyt
TI - Slice modules over minimal 2-fundamental algebras
JO - Open Mathematics
PY - 2007
VL - 5
IS - 1
SP - 164
EP - 180
AB - We consider a class of algebras whose Auslander-Reiten quivers have starting components that are not generalized standard. For these components we introduce a generalization of a slice and show that only in finitely many cases (up to isomorphism) a slice module is a tilting module.
LA - eng
KW - Minimal 2-fundamental algebra; Auslander-Reiten quiver; slice module; tilting module; minimal 2-fundamental algebras; Auslander-Reiten quivers; tilting modules; Auslander-Reiten components; postprojective slice modules; cotilting modules; hereditary algebras; preinjective slice modules
UR - http://eudml.org/doc/269709
ER -

References

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  13. [13] 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(1), (2004), pp. 111–144. Zbl1107.16022
  14. [14] C.M. Ringel: Tame algebras and integral quadratic forms, LNM 1099, Springer, Berlin, 1984. 
  15. [15] J. Schröer: “Modules without self-extensions over gentle algebras”, J. Algebra, Vol. 216, (1999), pp. 178–189. http://dx.doi.org/10.1006/jabr.1998.7696 
  16. [16] A. Skowroński: “Generalized standard Auslander-Reiten components”, J. Math. Soc. Japan, Vol. 46, (1994), pp. 517–543. http://dx.doi.org/10.2969/jmsj/04630517 Zbl0828.16011
  17. [17] 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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