Cycle-finite algebras Original Research Article

Let A be a finite-dimensional K-algebra over an algebraically closed field K and mod A be the category of finitely generated right A-modules. Following [1], A is said to be cycle-finite if, for every cycle M0 → m1 → … → Mn = M0 of non-zero non-isomorphisms between indecomposable modules in mod A, the morphisms on this cycle do not belong to the infinite power of the Jacobson radical of mod A. In this article we describe the supports of stable tubes of the Auslander-Reiten quivers of cycle-finite algebras. As a consequence we get that every cycle-finite algebra is of polynomial growth. Moreover, we prove some characterizations of domestic cycle-finite algebras.