The Grothendieck group of a cluster category.

DOI10.1016/j.jpaa.2007.04.007zbMath1148.16005arXivmath/0606518OpenAlexW2020149019MaRDI QIDQ2456382

Helmut Lenzing, Michael Barot, Dirk Kussin

Publication date: 18 October 2007

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0606518

zbMATH Keywords

hereditary algebrastriangulated categoriesGrothendieck groupsDynkin quiverscoherent sheaveshereditary categoriescanonical algebrascluster categoriesweighted projective linesfinite global dimensiontriangulated structurescluster tubes

Mathematics Subject Classification ID

Related Items (23)

Cluster algebras arising from cluster tubes I: integer vectors ⋮ Cluster structures from 2-Calabi-Yau categories with loops ⋮ Categorical webs and \(S\)-duality in 4d \({\mathcal {N}} = 2\) QFT ⋮ Algebras of finite representation type arising from maximal rigid objects ⋮ A geometric model of tube categories. ⋮ Maximal rigid subcategories in 2-Calabi-Yau triangulated categories. ⋮ Graded cluster algebras ⋮ Triangulated quotient categories revisited ⋮ NEARLY MORITA EQUIVALENCES AND RIGID OBJECTS ⋮ Homotopy invariants of singularity categories ⋮ Endomorphism Algebras of Maximal Rigid Objects in Cluster Tubes ⋮ Graded Frobenius cluster categories ⋮ Denominators in cluster algebras of affine type. ⋮ The cluster category of a canonical algebra ⋮ Homological classification of 4d \(\mathcal{N} = 2\) QFT. Rank-1 revisited ⋮ Grothendieck group and generalized mutation rule for 2-Calabi-Yau triangulated categories ⋮ Extensions of covariantly finite subcategories revisited ⋮ From triangulated categories to module categories via localisation ⋮ Cluster algebras arising from cluster tubes ⋮ Lifting to maximal rigid objects in 2-Calabi-Yau triangulated categories ⋮ Cluster algebras arising from cluster tubes. II: the Caldero-Chapoton map ⋮ \(\mathbb{A}^1\)-homotopy invariants of dg orbit categories ⋮ On Modules over Endomorphism Algebras of Maximal Rigid Objects in 2-Calabi-Yau Triangulated Categories

Cites Work

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• Tame algebras and integral quadratic forms
• Tilting theory and cluster combinatorics.
• On triangulated orbit categories
• Cluster algebras I: Foundations
• On the K-theory of tubular algebras
• A characterization of hereditary categories with tilting object

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