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arXiv · 1706.06778

A geometric realization of the $m$-cluster categories of type $\tilde{D_n}$

Lucie Jacquet-Malo
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Abstract

We show that a subcategory of the $m$-cluster category of type $\tilde{D_n}$ is isomorphic to a category consisting of arcs in an $(n-2)m$-gon with two central $(m-1)$-gons inside of it. 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 $\tilde{D_7}$.

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BibTeXRIS

Lucie Jacquet-Malo. 2017-06-21. A geometric realization of the $m$-cluster categories of type $\tilde{D_n}$. https://arxiv.org/abs/1706.06778

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