Domestic iterated one-point extensions of algebras by two-ray modules

Grzegorz Bobiński; Andrzej Skowroński

Open Mathematics (2003)

  • Volume: 1, Issue: 4, page 457-476
  • ISSN: 2391-5455

Abstract

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In the paper, we introduce a wide class of domestic finite dimensional algebras over an algebraically closed field which are obtained from the hereditary algebras of Euclidean type , n≥1, by iterated one-point extensions by two-ray modules. We prove that these algebras are domestic and their Auslander-Reiten quivers admit infinitely many nonperiodic connected components with infinitely many orbits with respect to the action of the Auslander-Reiten translation. Moreover, we exhibit a wide class of almost sincere domestic simply connected algebras of large global dimensions.

How to cite

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Grzegorz Bobiński, and Andrzej Skowroński. "Domestic iterated one-point extensions of algebras by two-ray modules." Open Mathematics 1.4 (2003): 457-476. <http://eudml.org/doc/268930>.

@article{GrzegorzBobiński2003,
abstract = {In the paper, we introduce a wide class of domestic finite dimensional algebras over an algebraically closed field which are obtained from the hereditary algebras of Euclidean type , n≥1, by iterated one-point extensions by two-ray modules. We prove that these algebras are domestic and their Auslander-Reiten quivers admit infinitely many nonperiodic connected components with infinitely many orbits with respect to the action of the Auslander-Reiten translation. Moreover, we exhibit a wide class of almost sincere domestic simply connected algebras of large global dimensions.},
author = {Grzegorz Bobiński, Andrzej Skowroński},
journal = {Open Mathematics},
keywords = {16G20; 16G60; 16G70},
language = {eng},
number = {4},
pages = {457-476},
title = {Domestic iterated one-point extensions of algebras by two-ray modules},
url = {http://eudml.org/doc/268930},
volume = {1},
year = {2003},
}

TY - JOUR
AU - Grzegorz Bobiński
AU - Andrzej Skowroński
TI - Domestic iterated one-point extensions of algebras by two-ray modules
JO - Open Mathematics
PY - 2003
VL - 1
IS - 4
SP - 457
EP - 476
AB - In the paper, we introduce a wide class of domestic finite dimensional algebras over an algebraically closed field which are obtained from the hereditary algebras of Euclidean type , n≥1, by iterated one-point extensions by two-ray modules. We prove that these algebras are domestic and their Auslander-Reiten quivers admit infinitely many nonperiodic connected components with infinitely many orbits with respect to the action of the Auslander-Reiten translation. Moreover, we exhibit a wide class of almost sincere domestic simply connected algebras of large global dimensions.
LA - eng
KW - 16G20; 16G60; 16G70
UR - http://eudml.org/doc/268930
ER -

References

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