<p>As a generalization of support <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10998_2025_653_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(\tau \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>τ</mi> </math></EquationSource> </InlineEquation>-tilting modules, H. Enomoto introduced the notion of wide <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10998_2025_653_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(\tau \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>τ</mi> </math></EquationSource> </InlineEquation>-tilting modules and established a bijection between wide <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10998_2025_653_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(\tau \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>τ</mi> </math></EquationSource> </InlineEquation>-tilting modules and doubly functorially finite ICE-closed subcategories, which extended Adachi-Iyama-Reiten’s bijection on torsion classes. In this paper, we consider the relationship between wide <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10998_2025_653_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(\tau \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>τ</mi> </math></EquationSource> </InlineEquation>-tilting modules and some sets of bricks (named epibricks). In particular, we show that there is a bijection between wide <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10998_2025_653_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(\tau \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>τ</mi> </math></EquationSource> </InlineEquation>-tilting modules and epibricks for Nakayama algebras. As a consequence, we get a recurrence relation for the number of wide <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10998_2025_653_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(\tau \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>τ</mi> </math></EquationSource> </InlineEquation>-tilting modules over Nakayama algebras.</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 note on wide \(\tau \)-tilting modules and epibricks

  • Hanpeng Gao

摘要

As a generalization of support \(\tau \) τ -tilting modules, H. Enomoto introduced the notion of wide \(\tau \) τ -tilting modules and established a bijection between wide \(\tau \) τ -tilting modules and doubly functorially finite ICE-closed subcategories, which extended Adachi-Iyama-Reiten’s bijection on torsion classes. In this paper, we consider the relationship between wide \(\tau \) τ -tilting modules and some sets of bricks (named epibricks). In particular, we show that there is a bijection between wide \(\tau \) τ -tilting modules and epibricks for Nakayama algebras. As a consequence, we get a recurrence relation for the number of wide \(\tau \) τ -tilting modules over Nakayama algebras.