On the radical of cluster tilted algebras

Abstract

We determine the minimal lower bound n, with \(n \geqslant 1\), where the n-th power of the radical of the module category of a representation-finite cluster tilted algebra vanishes. We give such a bound in terms of the number of vertices of the underline quiver. Consequently, we get the nilpotency index of the radical of the module category for representation-finite self-injective cluster tilted algebras. We also study the non-zero composition of m, \(m \geqslant 2\), irreducible morphisms between indecomposable modules in representation-finite cluster tilted algebras lying in the \((m\,{+}\,1)\)-th power of the radical of their module category.