Mathematics – Representation Theory
Scientific paper
2009-02-24
Mathematics
Representation Theory
20 pages
Scientific paper
This paper investigates a certain 2-Calabi-Yau triangulated category D whose Auslander-Reiten quiver is ZA_{\infty}. We show that the cluster tilting subcategories of D form a so-called cluster structure, and we classify these subcategories in terms of what one may call `triangulations of the infinity-gon'. This is reminiscent of the cluster category C of type A_n which is a 2-Calabi-Yau triangulated category whose Auslander-Reiten quiver is a quotient of ZA_n. The cluster tilting subcategories of C form a cluster structure and they are classified in terms of triangulations of the (n+3)-gon. The category D behaves like a `cluster category of type A_{\infty}'.
Holm Thorsten
Jorgensen Peter
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