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.
@article{bwmeta1.element.doi-10_2478_BF02475954,
author = {Otto Kerner and Andrzej Skowro\'nski and Kunio Yamagata and Dan Zacharia},
title = {Finiteness of the strong global dimension of radical square zero algebras},
journal = {Open Mathematics},
volume = {2},
year = {2004},
pages = {103-111},
zbl = {1061.16011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02475954}
}
Otto Kerner; Andrzej Skowroński; Kunio Yamagata; Dan Zacharia. Finiteness of the strong global dimension of radical square zero algebras. Open Mathematics, Tome 2 (2004) pp. 103-111. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02475954/
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