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<p>We determine the primitive-ideal spaces, and hence the ideal lattices, of a large class of <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="208_2024_3076_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(C^*\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mo>∗</mo> </msup> </math></EquationSource> </InlineEquation>-algebras arising from commuting local homeomorphisms. This class contains the <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="208_2024_3076_Article_IEq5.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(C^*\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mo>∗</mo> </msup> </math></EquationSource> </InlineEquation>-algebra of any row-finite 2-graph without sources. A key ingredient is the notion of harmonious families of bisections in étale groupoids arising from finite families of commuting local homeomorphisms.</p>

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Ideal structure of \(C^*\)-algebras of commuting local homeomorphisms

  • 期刊论文

  • 发表日期：

    2025年1月17日

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  • Kevin Aguyar Brix,
  • Toke Meier Carlsen,
  • Aidan Sims

摘要

We determine the primitive-ideal spaces, and hence the ideal lattices, of a large class of \(C^*\) C ∗ -algebras arising from commuting local homeomorphisms. This class contains the \(C^*\) C ∗ -algebra of any row-finite 2-graph without sources. A key ingredient is the notion of harmonious families of bisections in étale groupoids arising from finite families of commuting local homeomorphisms.