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<p>We prove an equivariant index theorem on the Euclidean space using a continuous field of <i>C</i>*-algebras. This generalizes the work of Elliott et al. (1996), which is a special case of the algebraic index theorem by Nest and Tsygan (1995). Using our formula, we see that the equivariant index of the Bott-Dirac operator on ℝ<sup>2<i>n</i></sup> can be explicitly calculated.</p>

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An equivariant index theorem on ℝn in the context of continuous fields of C*-algebras

  • 期刊论文

  • 发表日期：

    2025年1月3日

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  • Baiying Ren,
  • Hang Wang,
  • Zijing Wang

摘要

We prove an equivariant index theorem on the Euclidean space using a continuous field of C*-algebras. This generalizes the work of Elliott et al. (1996), which is a special case of the algebraic index theorem by Nest and Tsygan (1995). Using our formula, we see that the equivariant index of the Bott-Dirac operator on ℝ2n can be explicitly calculated.