$\tilde{A}$ and $\tilde{D}$ type cluster algebras: Triangulated surfaces and friezes

DOI10.1007/S10801-022-01152-ZzbMATH Open1509.13033arXiv2105.11682MaRDI QIDQ6368452

Joe Pallister

Publication date: 25 May 2021

Abstract: By viewing $ildeA$ and $ildeD$ type cluster algebras as triangulated surfaces, we find all cluster variables in terms of either (i) the frieze pattern (or bipartite belt) or (ii) the periodic quantities previously found for the cluster map associated with these frieze patterns. We show that these cluster variables form friezes which are precisely the ones found in [1] by applying the cluster character to the associated cluster category.

Mathematics Subject Classification ID

Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers (16G70) Cluster algebras (13F60) Completely integrable discrete dynamical systems (37J70)

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