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<p> <?tk 3?>Let <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41478_2025_989_Article_IEq4.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="89" /> </InlineMediaObject> <EquationSource Format="TEX">\(G_0=K\ltimes \mathfrak {p}\)</EquationSource> </InlineEquation> be the Cartan motion groups. In this paper, we describe the <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41478_2025_989_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(C^*\)</EquationSource> </InlineEquation>-algebra <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41478_2025_989_Article_IEq6.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="53" /> </InlineMediaObject> <EquationSource Format="TEX">\(C^*(G_0)\)</EquationSource> </InlineEquation> of <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41478_2025_989_Article_IEq7.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(G_0\)</EquationSource> </InlineEquation> in terms of a <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41478_2025_989_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="22" /> </InlineMediaObject> <EquationSource Format="TEX">\(C^*\)</EquationSource> </InlineEquation>-algebra of operator fields defined over its dual space.</p>

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The \(C^*\)-algebra of Cartan motion groups

  • 期刊论文

  • 发表日期：

    2025年10月23日

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  • Hedi Regeiba,
  • Aymen Rahali

摘要

Let \(G_0=K\ltimes \mathfrak {p}\) be the Cartan motion groups. In this paper, we describe the \(C^*\) -algebra \(C^*(G_0)\) of \(G_0\) in terms of a \(C^*\) -algebra of operator fields defined over its dual space.