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<p>Motivated by the study of the <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(C^*\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mo>∗</mo> </msup> </math></EquationSource> </InlineEquation>-algebras of the nilpotent Lie groups of upper triangular matrices <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(N_3\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>N</mi> <mn>3</mn> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(N_4\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>N</mi> <mn>4</mn> </msub> </math></EquationSource> </InlineEquation>, we investigate the structure of the <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(C^*\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mo>∗</mo> </msup> </math></EquationSource> </InlineEquation>-algebra of <InlineEquation ID="IEq10"> <EquationSource Format="TEX">\(N_5\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>N</mi> <mn>5</mn> </msub> </math></EquationSource> </InlineEquation>. We describe it as an algebra of operator fields defined over its spectrum and establish the norm control of dual limits condition.</p>

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The \(C^*\)-algebra of the nilpotent Lie group of upper triangular matrices \(N_5\).

  • 期刊论文

  • 发表日期：

    2026年1月20日

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  • Hedi Regeiba,
  • Ghofrane Kardi

摘要

Motivated by the study of the \(C^*\) C ∗ -algebras of the nilpotent Lie groups of upper triangular matrices \(N_3\) N 3 and \(N_4\) N 4 , we investigate the structure of the \(C^*\) C ∗ -algebra of \(N_5\) N 5 . We describe it as an algebra of operator fields defined over its spectrum and establish the norm control of dual limits condition.