On the radical of Cluster tilted algebras

CHAIO, CLAUDIA Y GUAZZELLI, VICTORIA.

European Journal of Mathematics

Springer

Lugar: Suiza; Año: 2022 vol. 8 p. 640 - 654

2199-675X

We determine the minimal lower bound n, with n ≥ 1, where the n-th power of theradical of the module category of a representation-finite cluster tilted algebra vanishes. We givesuch a bound in terms of the number of vertices of the underline quiver. Consequently, we get thenilpotency index of the radical of the module category for representation-finite self-injective clustertilted algebras. We also study the non-zero composition of m, m ≥ 2, irreducible morphisms betweenindecomposable modules in representation-finite cluster tilted algebras lying in the (m+1)-th powerof the radical of their module category.