Finiteness of the strong global dimension of radical square zero algebras

Otto Kerner; Andrzej Skowroński; Kunio Yamagata; Dan Zacharia

Open Mathematics (2004)

  • Volume: 2, Issue: 1, page 103-111
  • ISSN: 2391-5455

Abstract

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The strong global dimension of a finite dimensional algebra A is the maximum of the width of indecomposable bounded differential complexes of finite dimensional projective A-modules. We prove that the strong global dimension of a finite dimensional radical square zero algebra A over an algebraically closed field is finite if and only if A is piecewise hereditary. Moreover, we discuss results concerning the finiteness of the strong global dimension of algebras and the related problem on the density of the push-down functors associated to the canonical Galois coverings of the trivial extensions of algebras by their repetitive algebras.

How to cite

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Otto Kerner, et al. "Finiteness of the strong global dimension of radical square zero algebras." Open Mathematics 2.1 (2004): 103-111. <http://eudml.org/doc/268840>.

@article{OttoKerner2004,
abstract = {The strong global dimension of a finite dimensional algebra A is the maximum of the width of indecomposable bounded differential complexes of finite dimensional projective A-modules. We prove that the strong global dimension of a finite dimensional radical square zero algebra A over an algebraically closed field is finite if and only if A is piecewise hereditary. Moreover, we discuss results concerning the finiteness of the strong global dimension of algebras and the related problem on the density of the push-down functors associated to the canonical Galois coverings of the trivial extensions of algebras by their repetitive algebras.},
author = {Otto Kerner, Andrzej Skowroński, Kunio Yamagata, Dan Zacharia},
journal = {Open Mathematics},
keywords = {Primary 16D50; 16E10; 18E30; Secondary 16G10},
language = {eng},
number = {1},
pages = {103-111},
title = {Finiteness of the strong global dimension of radical square zero algebras},
url = {http://eudml.org/doc/268840},
volume = {2},
year = {2004},
}

TY - JOUR
AU - Otto Kerner
AU - Andrzej Skowroński
AU - Kunio Yamagata
AU - Dan Zacharia
TI - Finiteness of the strong global dimension of radical square zero algebras
JO - Open Mathematics
PY - 2004
VL - 2
IS - 1
SP - 103
EP - 111
AB - The strong global dimension of a finite dimensional algebra A is the maximum of the width of indecomposable bounded differential complexes of finite dimensional projective A-modules. We prove that the strong global dimension of a finite dimensional radical square zero algebra A over an algebraically closed field is finite if and only if A is piecewise hereditary. Moreover, we discuss results concerning the finiteness of the strong global dimension of algebras and the related problem on the density of the push-down functors associated to the canonical Galois coverings of the trivial extensions of algebras by their repetitive algebras.
LA - eng
KW - Primary 16D50; 16E10; 18E30; Secondary 16G10
UR - http://eudml.org/doc/268840
ER -

References

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