We characterize the modules of infinite projective dimension over the endomorphism algebras of Oppermann–Thomas cluster-tilting objects in -angulated categories . For an indecomposable object of , we define in this article the ideal of given by all endomorphisms that factor through , and show that the -module has infinite projective dimension precisely when is nonzero. As an application, we generalize a recent result by Beaudet–Brüstle–Todorov for cluster-tilted algebras.
"Modules of infinite projective dimension." Rocky Mountain J. Math. 52 (2) 749 - 755, April 2022. https://doi.org/10.1216/rmj.2022.52.749