English

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

Representation Theory 2021-10-01 v5 Category Theory

Abstract

We show that a subcategory of the mm-cluster category of type Dn~\tilde{D_n} is isomorphic to a category consisting of arcs in an (n2)m(n-2)m-gon with two central (m1)(m-1)-gons inside of it. We show that the mutation of colored quivers and mm-cluster-tilting objects is compatible with the flip of an (m+2)(m+2)-angulation. In the final part of this paper, we detail an example of a quiver of type D7~\tilde{D_7}.

Keywords

Cite

@article{arxiv.1706.06778,
  title  = {A geometric realization of the $m$-cluster categories of type $\tilde{D_n}$},
  author = {Lucie Jacquet-Malo},
  journal= {arXiv preprint arXiv:1706.06778},
  year   = {2021}
}