Lifting to Cluster-tilting Objects in Higher Cluster Categories

DOI10.1142/S1005386712000582zbMath1314.18014arXiv0810.3360OpenAlexW2963420479MaRDI QIDQ2859258

Pin Liu

Publication date: 7 November 2013

Published in: Algebra Colloquium (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0810.3360

zbMATH Keywords

tilting modulesCalabi-Yau category\(d\)-cluster-tilting objectshigher cluster category

Mathematics Subject Classification ID

Module categories in associative algebras (16D90) Derived categories and associative algebras (16E35)

Related Items (1)

Lifting to relative cluster tilting objects in $2n$-Calabi–Yau $(n+2)$-angulated categories

Cites Work

• Coloured quiver mutation for higher cluster categories.
• Higher-dimensional Auslander-Reiten theory on maximal orthogonal subcategories.
• Cluster-tilted algebras are Gorenstein and stably Calabi-Yau
• On the relation between cluster and classical tilting.
• Rigid objects in higher cluster categories
• Cluster algebras. II: Finite type classification
• Cluster algebras. III: Upper bounds and double Bruhat cells.
• Cluster combinatorics of \(d\)-cluster categories.
• Generalized cluster complexes via quiver representations.
• Defining an \(m\)-cluster category.
• Mutation in triangulated categories and rigid Cohen-Macaulay modules
• Tilting theory and cluster combinatorics.
• Noetherian hereditary abelian categories satisfying Serre duality
• Cluster algebras I: Foundations
• Lifting to Cluster-Tilting Objects in 2-Calabi–Yau Triangulated Categories
• Cluster-tilted algebras
• Cluster algebras IV: Coefficients
• Quivers with relations arising from clusters (𝐴_{𝑛} case)

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