A Geometric Realization of the m-cluster Category of Affine Type A

Abstract

We give a geometric realization of a subcategory of the m-cluster category 𝒞 ^m of type , by using (m + 2)-angulations of an annulus with p + q marked points. We also give a bijection between an equivalence class of (m + 2)-angulations and the mutation class of coloured quivers of type .

Key Words:

• Cluster algebra
• Cluster-tilting
• Coloured quiver
• m-cluster category
• Quiver mutation

2010 Mathematics Subject Classification:

• Primary: 16G20, 16G70, 18E30
• Secondary: 05E15, 05A19

ACKNOWLEDGMENTS

The author would like to thank the anonymous referee for helpful suggestions.

Notes

Communicated by S. Bazzoni.