We define a notion of left section in an Auslander-Reiten component, by weakening one of the axioms for sections. We derive a generalisation of the Liu-Skowroński criterion for tilted algebras, then apply our results to describe the Auslander-Reiten components lying in the left part of an artin algebra.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm116-2-10,
author = {Ibrahim Assem},
title = {Left sections and the left part of an artin algebra},
journal = {Colloquium Mathematicae},
volume = {116},
year = {2009},
pages = {273-300},
zbl = {1239.16022},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm116-2-10}
}
Ibrahim Assem. Left sections and the left part of an artin algebra. Colloquium Mathematicae, Tome 116 (2009) pp. 273-300. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm116-2-10/