A characterization of representation-finite algebras
Volume 140 / 1991
Fundamenta Mathematicae 140 (1991), 31-34
DOI: 10.4064/fm-140-1-31-34
Abstract
Let A be a finite-dimensional, basic, connected algebra over an algebraically closed field. Denote by Γ(A) the Auslander-Reiten quiver of A. We show that A is representation-finite if and only if Γ(A) has at most finitely many vertices lying on oriented cycles and finitely many orbits with respect to the action of the Auslander-Reiten translation.
