Scholarlink

<p>We show that a subcategory of the <i>m</i>-cluster category of type <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11464_2023_133_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\({\tilde D}_{n}\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <msub> <mrow> <mrow> <mover> <mi>D</mi> <mo stretchy="false">∼</mo> </mover> </mrow> </mrow> <mrow> <mi>n</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> is isomorphic to a category consisting of arcs in an (<i>n</i> − 2)<i>m</i>-gon with two central (<i>m</i> − 1)-gons in its interior. We show that the mutation of colored quivers and <i>m</i>-cluster-tilting objects is compatible with the flip of an (<i>m</i> + 2)-angulation. In the final part of this paper, we detail an example of a quiver of type <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11464_2023_133_Article_IEq3.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\({\tilde D}_{7}\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <msub> <mrow> <mrow> <mover> <mi>D</mi> <mo stretchy="false">∼</mo> </mover> </mrow> </mrow> <mrow> <mn>7</mn> </mrow> </msub> </math></EquationSource> </InlineEquation>.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

A Geometric Realization of the m-cluster Categories of Type \({\tilde D}_{n}\)

  • 期刊论文

  • 发表日期：

    2025年1月5日

查看全文
  • Lucie Jacquet-Malo

摘要

We show that a subcategory of the m-cluster category of type \({\tilde D}_{n}\) D ∼ n 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 \({\tilde D}_{7}\) D ∼ 7 .