Mutation in triangulated categories and rigid Cohen-Macaulay modules

Abstract

We introduce the notion of mutation of $n$-cluster tilting subcategories in a triangulated category with Auslander-Reiten-Serre duality. Using this idea, we are able to obtain the complete classifications of rigid Cohen-Macaulay modules over certain Veronese subrings.

52 pages. To appear in Invent. Math

Cited by in corpus (76)

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• Cluster categories for marked surfaces: punctured case
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• Auslander-Buchweitz context and co-t-structures
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• d-Representation-finite self-injective algebras
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• From triangulated categories to module categories via localisation
• Classifying $\tau$-tilting modules over the Auslander algebra of $K[x]/(x^n)$
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• Homological Classification of 4d $\mathcal{N}=2$ QFT. Part I: Rank-1 revisited
• Crossed-products of Calabi-Yau algebras by finite groups
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• Abelian categories arising from cluster tilting subcategories
• The category of extensions and a characterisation of $n$-exangulated functors
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• Calabi-Yau properties of Postnikov diagrams
• $t$-Analog of $q$-Characters, Bases of Quantum Cluster Algebras, and a Correction Technique
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• Cluster algebras arising from cluster tubes
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• Abelian categories from triangulated categories via Nakaoka-Palu's localization
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• Mutation of torsion pairs in cluster categories of Dynkin type $D$
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