On the relation between cluster and classical tilting

2008/10/02 by Thorsten Holm, Holm, Thorsten, Peter Jørgensen +1
Mathematics · #16G70 #18E10 #18E30 #18G99 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.0810.0411

openalex publication_date 2008/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let D be a triangulated category with a cluster tilting subcategory U. The quotient category D/U is abelian; suppose that it has finite global dimension. We show that projection from D to D/U sends cluster tilting subcategories of D to support tilting subcategories of D/U, and that, in turn, support tilting subcategories of D/U can be lifted uniquely to maximal 1-orthogonal subcategories of D.

Related

• From triangulated categories to abelian categories--cluster tilting in a general framework
• Relative cluster tilting theory and τ-tilting theory
• Projectively generated d-abelian categories are d-cluster tilting
• Lifting to cluster-tilting objects in 2-Calabi-Yau triangulated categories
• Proper abelian subcategories of triangulated categories and their tilting theory