Existence of cycle-finite algebras of infinite representation type without directing projective or injective modules
Tom 148 / 2017
Colloquium Mathematicum 148 (2017), 165-190 MSC: Primary 16G10, 16G70; Secondary 16G60. DOI: 10.4064/cm7190-2-2017 Opublikowany online: 24 April 2017
We solve an open problem concerning the existence of cycle-finite algebras of infinite representation type for which all indecomposable projective modules and indecomposable injective modules are nondirecting (lie on oriented cycles of indecomposable modules). We prove that there exist such algebras having large numbers of almost acyclic Auslander–Reiten components with finite cyclic multisections.