Continuous cluster categories of type D

Abstract

We construct continuous Frobenius categories of type $D$. The stable categories of these Frobenius categories are cluster categories which contain the standard cluster categories of type $D_n$. When $n=\infty$, maximal compatible sets of indecomposable objects are laminations of the punctured disk. Discrete laminations are clusters. This new construction is topological and it also gives an algebraic interpretation of the "tagged arcs" which occur in Schiffler's geometric description of clusters of type $D_n$.

41 pages, 11 figures

References in corpus (4)

• Cluster algebras and triangulated orbifolds
• Continuous cluster categories I
• Realising higher cluster categories of Dynkin type as stable module categories
• Cluster categories coming from cyclic posets

Cited by in corpus (4)

• Continuous Quivers of Type A (III) Embeddings of Cluster Theories
• Continuous Quivers of Type A (IV) Continuous Mutation and Geometric Models of $\mathbf{E}$-clusters
• Continuously triangulating the continuous cluster category
• Cluster categories coming from cyclic posets