Recollements and n -cluster tilting subcategories
type: Item
instance of: scholarly article
title: Recollements and n -cluster tilting subcategories
zbMATH Open document ID: 1547.18023
DOI: 10.1080/00927872.2024.2338489
author: Q6594902
author: Xiaoxiang Zhang
author: Yukun Zhou
published in: Communications in Algebra
publication date: 2024-08-29T00:00:00Z
review text: In this paper, the authors explore the intricate relations between three \(n\)-cluster tilting subcategories in a recollement of triangulated categories. Consider a recollement \((\mathcal D',\mathcal D,\mathcal D'')\) of triangulated categories.They demonstrate how an \(n\)-cluster tilting subcategory of can be constructed by gluing together \(n\)-cluster tilting subcategories of \(\mathcal D'\) and \(\mathcal D''\) under specific conditions. Conversely, they establish that an \(n\)-cluster tilting subcategory of \(\mathcal D\) induces corresponding \(n\)-cluster tilting subcategories in \(\mathcal D'\) and \(\mathcal D''\). These results lead to a one-to-one correspondence between certain \(n\)-cluster tilting subcategories of \(\mathcal D\) and pairs of such subcategories in \(\mathcal D'\) and \(\mathcal D''\). Additionally, they derive a recollement of abelian categories from this recollement of triangulated categories, revealing deeper structural connections.
reviewed by: Panyue Zhou
Mathematics Subject Classification ID: 18G80
Mathematics Subject Classification ID: 18A40
zbMATH DE Number: 7903256
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 7903256