A minimal non-tilted triangular algebra such that any proper semiconvex subcategory is tilted is called a tilt-semicritical algebra. We study the tilt-semicritical algebras which are quasitilted or one-point extensions of tilted algebras of tame hereditary type. We establish inductive procedures to decide whether or not a given strongly simply connected algebra is tilted.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm111-1-7, author = {Fl\'avio U. Coelho and Jos\'e A. de la Pe\~na and Sonia Trepode}, title = {On minimal non-tilted algebras}, journal = {Colloquium Mathematicae}, volume = {111}, year = {2008}, pages = {71-84}, zbl = {1135.16020}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm111-1-7} }
Flávio U. Coelho; José A. de la Peña; Sonia Trepode. On minimal non-tilted algebras. Colloquium Mathematicae, Tome 111 (2008) pp. 71-84. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm111-1-7/