Repetitive cluster categories of type Dn

Abstract

In this paper, we show that the repetitive cluster category of type $D_n$, defined as the orbit category ${\mathcal{D}}^b(\mathrm{mod}K{D}_n)/({\tau }^{-1}[1]{)}^p$, is equivalent to a category defined on a subset of tagged edges in a regular punctured polygon. This generalizes the construction of Schiffler, \cite{S}, which we recover when $p=1$.

arXiv admin note: substantial text overlap with arXiv:1201.1767, arXiv:math/0608264 by other authors