The representation dimension of domestic weakly symmetric algebras

Rafał Bocian; Thorsten Holm; Andrzej Skowroński

Open Mathematics (2004)

  • Volume: 2, Issue: 1, page 67-75
  • ISSN: 2391-5455

Abstract

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Auslander’s representation dimension measures how far a finite dimensional algebra is away from being of finite representation type. In [1], M. Auslander proved that a finite dimensional algebra A is of finite representation type if and only if the representation dimension of A is at most 2. Recently, R. Rouquier proved that there are finite dimensional algebras of an arbitrarily large finite representation dimension. One of the exciting open problems is to show that all finite dimensional algebras of tame representation type have representation dimension at most 3. We prove that this is true for all domestic weakly symmetric algebras over algebraically closed fields having simply connected Galois coverings.

How to cite

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Rafał Bocian, Thorsten Holm, and Andrzej Skowroński. "The representation dimension of domestic weakly symmetric algebras." Open Mathematics 2.1 (2004): 67-75. <http://eudml.org/doc/268908>.

@article{RafałBocian2004,
abstract = {Auslander’s representation dimension measures how far a finite dimensional algebra is away from being of finite representation type. In [1], M. Auslander proved that a finite dimensional algebra A is of finite representation type if and only if the representation dimension of A is at most 2. Recently, R. Rouquier proved that there are finite dimensional algebras of an arbitrarily large finite representation dimension. One of the exciting open problems is to show that all finite dimensional algebras of tame representation type have representation dimension at most 3. We prove that this is true for all domestic weakly symmetric algebras over algebraically closed fields having simply connected Galois coverings.},
author = {Rafał Bocian, Thorsten Holm, Andrzej Skowroński},
journal = {Open Mathematics},
keywords = {Primary 16D50; 16E10; 16G60; Secondary 16G10; 18E30},
language = {eng},
number = {1},
pages = {67-75},
title = {The representation dimension of domestic weakly symmetric algebras},
url = {http://eudml.org/doc/268908},
volume = {2},
year = {2004},
}

TY - JOUR
AU - Rafał Bocian
AU - Thorsten Holm
AU - Andrzej Skowroński
TI - The representation dimension of domestic weakly symmetric algebras
JO - Open Mathematics
PY - 2004
VL - 2
IS - 1
SP - 67
EP - 75
AB - Auslander’s representation dimension measures how far a finite dimensional algebra is away from being of finite representation type. In [1], M. Auslander proved that a finite dimensional algebra A is of finite representation type if and only if the representation dimension of A is at most 2. Recently, R. Rouquier proved that there are finite dimensional algebras of an arbitrarily large finite representation dimension. One of the exciting open problems is to show that all finite dimensional algebras of tame representation type have representation dimension at most 3. We prove that this is true for all domestic weakly symmetric algebras over algebraically closed fields having simply connected Galois coverings.
LA - eng
KW - Primary 16D50; 16E10; 16G60; Secondary 16G10; 18E30
UR - http://eudml.org/doc/268908
ER -

References

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