Repetitive cluster categories of type $$D_n$$

Abstract

In this paper, we show that the repetitive cluster category of type $$D_n$$ , defined as the orbit category $$\mathcal {D}^b(\mathrm {mod} {\textsf {k}}D_n)/(\tau ^{-1}[1])^p$$ , is equivalent to a category defined on a subset of tagged edges in a regular punctured polygon. This generalizes the construction of Schiffler, [17], which we recover when $$p=1$$ .