Scholarlink

<p>We propose a mutation formula for the general rank from a principal component <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10468_2024_10306_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="47" /> </InlineMediaObject> <EquationSource Format="TEX">\({{\,\textrm{PC}\,}}(\delta )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow> <mspace width="0.166667em" /> <mtext>PC</mtext> <mspace width="0.166667em" /> </mrow> <mo stretchy="false">(</mo> <mi>δ</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> of representations to another one <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10468_2024_10306_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="46" /> </InlineMediaObject> <EquationSource Format="TEX">\({{\,\textrm{PC}\,}}({\epsilon })\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow> <mspace width="0.166667em" /> <mtext>PC</mtext> <mspace width="0.166667em" /> </mrow> <mo stretchy="false">(</mo> <mi>ϵ</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> for a quiver with potential. We give sufficient conditions for the formula to hold. In particular, the formula holds when any of <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10468_2024_10306_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(\delta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>δ</mi> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10468_2024_10306_Article_IEq4.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">\({\epsilon }\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ϵ</mi> </math></EquationSource> </InlineEquation> is reachable. We discover several related mutation invariants.</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

On the General Ranks of QP Representations

  • 期刊论文

  • 发表日期：

    2025年1月4日

查看全文
  • JiaRui Fei

摘要

We propose a mutation formula for the general rank from a principal component \({{\,\textrm{PC}\,}}(\delta )\) PC ( δ ) of representations to another one \({{\,\textrm{PC}\,}}({\epsilon })\) PC ( ϵ ) for a quiver with potential. We give sufficient conditions for the formula to hold. In particular, the formula holds when any of \(\delta \) δ and \({\epsilon }\) ϵ is reachable. We discover several related mutation invariants.