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arXiv · 1201.1767

Repetitive higher cluster categories of type A_n

L. Lamberti
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Abstract

We show that the repetitive higher cluster category of type A_n, defined as the orbit category D^b(mod kA_n)/(tau^{-1}[m])^p, is equivalent to a category defined on a subset of diagonals in a regular p(nm+1)-gon. This generalizes the construction of Caldero-Chapoton-Schiffler, which we recover when p=m=1, and the work of Baur-Marsh, treating the case p=1, m>1. Our approach also leads to a geometric model of the bounded derived category D^b(mod kA_n).

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L. Lamberti. 2013-01-10. Repetitive higher cluster categories of type A_n. https://doi.org/10.1142/s0219498813500916

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