Repetitive higher cluster categories of type A_n
Category Theory
2014-12-10 v2 Combinatorics
Representation Theory
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).
Keywords
Cite
@article{arxiv.1201.1767,
title = {Repetitive higher cluster categories of type A_n},
author = {L. Lamberti},
journal= {arXiv preprint arXiv:1201.1767},
year = {2014}
}