TILTING MUTATION FOR m-REPLICATED ALGEBRAS

DOI10.1142/S0219498811004744zbMath1264.16008arXiv0903.0958OpenAlexW2963182735MaRDI QIDQ3117888

Hongbo Lü, Shun-Hua Zhang

Publication date: 1 March 2012

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0903.0958

zbMATH Keywords

tilting modulesfinite-dimensional algebrasprojective dimensionhereditary algebrastriangulated categoriesAuslander-Reiten translationsbounded derived categoriescluster categoriestilting mutationstilting objectsreplicated algebrasexchange pairsmutation teams

Mathematics Subject Classification ID

Module categories in associative algebras (16D90) Homological functors on modules (Tor, Ext, etc.) in associative algebras (16E30) Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers (16G70) Representations of quivers and partially ordered sets (16G20) Representations of associative Artinian rings (16G10) Homological dimension in associative algebras (16E10)

Related Items (1)

Endomorphism algebras of tilting modules over \(m\)-replicated algebras.

Cites Work

• Tame algebras and integral quadratic forms
• Cluster categories and duplicated algebras.
• Partial tilting modules over \(m\)-replicated algebras.
• Cluster algebras. II: Finite type classification
• Cluster combinatorics of \(d\)-cluster categories.
• \(m\)-cluster categories and \(m\)-replicated algebras.
• Defining an \(m\)-cluster category.
• Mutation in triangulated categories and rigid Cohen-Macaulay modules
• Tilting theory and cluster combinatorics.
• Cluster algebras I: Foundations
• Complements to the Almost Complete TiltingA^(m)-Modules
• Tilting Mutation and Duplicated Algebras
• Quivers with relations arising from clusters (𝐴_{𝑛} case)

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