Geometric construction of cluster algebras and cluster categories

zbMATH Open1256.13013arXiv0804.4065MaRDI QIDQ2906575

Karin Baur

Publication date: 5 September 2012

Abstract: In this note we explain how to obtain cluster algebras from triangulations of (punctured) discs following the approach of S. Fomin, M. Shapiro and D. Thurston. Furthermore, we give a description of m-cluster categories via diagonals (arcs) in (punctured) polygons and of m-cluster categories via powers of translation quivers as given in joint work with R. Marsh.

Full work available at URL: https://arxiv.org/abs/0804.4065

zbMATH Keywords

translation quiverscluster algebrascluster categoriestriangulations of punctured discs

Mathematics Subject Classification ID

Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers (16G70) Representations of quivers and partially ordered sets (16G20) Cluster algebras (13F60)

Related Items (3)

A geometric model for cluster categories of type \(D_n\). ⋮ A Geometric Interpretation of the Triangulated Structure ofm-Cluster Categories ⋮ A Geometric Description of them-cluster Categories of TypeDn

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