A Geometric Realization of the m-cluster Categories of Type

Abstract

We show that a subcategory of the m-cluster category of type

{\stackrel{\sim }{D}}_n

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is isomorphic to a category consisting of arcs in an (n − 2)m-gon with two central (m − 1)-gons in its interior. We show that the mutation of colored quivers and m-cluster-tilting objects is compatible with the flip of an (m + 2)-angulation. In the final part of this paper, we detail an example of a quiver of type

{\stackrel{\sim }{D}}_7

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.

Keywords

Cluster algebras / m-cluster categories / tame quivers /

{\stackrel{\sim }{D}}_n

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')">

{\stackrel{\sim }{D}}_n

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/ 18E30 / 13F60 / 05C62

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Peking University