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<p>We investigate the use of labelled graphs as a Morita equivalence invariant for inverse semigroups. We construct a labelled graph from a combinatorial inverse semigroup <i>S</i> with 0 admitting a special set of idempotent <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="233_2025_10525_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathscr {D}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">D</mi> </math></EquationSource> </InlineEquation>-class representatives and show that <i>S</i> is Morita equivalent to a labelled graph inverse semigroup. For the inverse hull <i>S</i> of a Markov shift, we show that the labelled graph determines the Morita equivalence class of <i>S</i> among all other inverse hulls of Markov shifts.</p>

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Labelled graphs as Morita equivalence invariants for a class of inverse semigroups

  • 期刊论文

  • 发表日期：

    2025年4月15日

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  • Zachary Duah,
  • Stian Du Preez,
  • David Milan,
  • Shreyas Ramamurthy,
  • Lucas Vega

摘要

We investigate the use of labelled graphs as a Morita equivalence invariant for inverse semigroups. We construct a labelled graph from a combinatorial inverse semigroup S with 0 admitting a special set of idempotent \(\mathscr {D}\) D -class representatives and show that S is Morita equivalent to a labelled graph inverse semigroup. For the inverse hull S of a Markov shift, we show that the labelled graph determines the Morita equivalence class of S among all other inverse hulls of Markov shifts.