On a cluster category of type $D_{\infty}$

TL;DR

This paper investigates the canonical orbit category derived from the bounded derived category of type D_infinity quiver representations, establishing it as a cluster category with a well-defined cluster structure.

Contribution

It proves that the orbit category of the derived category of D_infinity quiver representations is a cluster category with cluster-tilting subcategories forming a cluster structure.

Findings

The orbit category is a cluster category.

Cluster-tilting subcategories form a cluster structure.

Extends cluster theory to infinite type D quivers.

Abstract

We study the canonical orbit category of the bounded derived category of finite dimensional representations of the quiver of type $D_{\infty}$. We prove that this orbit category is a cluster category, that is, its cluster-tilting subcategories form a cluster structure as defined in [\ref{BIRS}].