Combinatorial model for cluster categories of type E

Abstract

In this paper we give a geometric-combinatorial description of the cluster categories of type E. In particular, we give an explicit geometric description of all cluster tilting objects in the cluster category of type E_6. The model we propose here arises from combining two polygons, and it generalises the description of the cluster category of type A and D.

Following the suggestion of the referee we significantely extended Section 3, 4 and 6. To appear in the Journal of Algebraic Combinatorics

References in corpus (6)

• On triangulated orbit categories
• Quivers with relations arising from clusters (A_n case)
• On the Cluster Category of a Marked Surface
• Categorification of skew-symmetrizable cluster algebras
• Repetitive higher cluster categories of type A_n
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Cited by in corpus (3)

• Bases for cluster algebras from orbifolds
• Combinatorial model for m-cluster categories in type E
• A geometric model for the non-$\tau$-rigid modules of type ${\tilde{D}}_n$