Modules of infinite projective dimension

Abstract

We characterize the modules of infinite projective dimension over the endomorphism algebras of Opperman-Thomas cluster tilting objects X in (n + 2)-angulated categories (C, Σ n , Θ). We define in this article the ideal I M of End C (Σ n X) given by all endomorphisms that factor through M , and show that the End C (X)-module Hom C (X, M ) has infinite projective dimension precisely when I M is non-zero. As an application, we generalize a recent result by Beaudet-Brüstle-Todorov for cluster-tilted algebras.