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April 2022 Modules of infinite projective dimension
Panyue Zhou, Xingjia Zhou
Rocky Mountain J. Math. 52(2): 749-755 (April 2022). DOI: 10.1216/rmj.2022.52.749

Abstract

We characterize the modules of infinite projective dimension over the endomorphism algebras of Oppermann–Thomas cluster-tilting objects X in (n+2)-angulated categories (𝒞,Σn,Θ). For an indecomposable object M of 𝒞, we define in this article the ideal IM of End𝒞(ΣnX) given by all endomorphisms that factor through addM, and show that the End𝒞(X)-module Hom𝒞(X,M) has infinite projective dimension precisely when IM is nonzero. As an application, we generalize a recent result by Beaudet–Brüstle–Todorov for cluster-tilted algebras.

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Panyue Zhou. Xingjia Zhou. "Modules of infinite projective dimension." Rocky Mountain J. Math. 52 (2) 749 - 755, April 2022. https://doi.org/10.1216/rmj.2022.52.749

Information

Received: 28 July 2020; Revised: 2 July 2021; Accepted: 17 July 2021; Published: April 2022
First available in Project Euclid: 17 May 2022

Digital Object Identifier: 10.1216/rmj.2022.52.749

Subjects:
Primary: 16D90 , 18G80

Keywords: (n+2)-angulated categories , cluster-tilting objects , projective dimension

Rights: Copyright © 2022 Rocky Mountain Mathematics Consortium

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Vol.52 • No. 2 • April 2022
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