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A geometric realization of the \(m\)-cluster category of affine type \(A\). (English) Zbl 1338.16020

Summary: We give a geometric realization of a subcategory of the \(m\)-cluster category \(\mathcal C^m\) of type \(\widetilde A_{p,q}\), by using \((m+2)\)-angulations of an annulus with \(p+q\) marked points. We also give a bijection between an equivalence class of \((m+2)\)-angulations and the mutation class of coloured quivers of type \(\widetilde A_{p,q}\).

MSC:

16G20 Representations of quivers and partially ordered sets
16G70 Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers
18E30 Derived categories, triangulated categories (MSC2010)
05E15 Combinatorial aspects of groups and algebras (MSC2010)
13F60 Cluster algebras
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