Equivariant Index Theorem on $\mathbb{R}^n$ in the Context of Continuous Fields of $C^*$-algebras

Baiying Ren; Hang Wang; Zijing Wang

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arXiv · 2401.07474

Equivariant Index Theorem on $\mathbb{R}^n$ in the Context of Continuous Fields of $C^*$-algebras

Baiying Ren·Hang Wang·Zijing Wang

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Abstract

We prove an equivariant index theorem on the Euclidean space using a continuous field of $C^*$-algebras. This generalizes the work of Elliott, Natsume and Nest, which is a special case of the algebraic index theorem by Nest-Tsygan. Using our formula, the equivariant index of the Bott-Dirac operator on $\mathbb{R}^{2n}$ can be explicitly calculated.

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Baiying Ren, Hang Wang, Zijing Wang. 2024-01-15. Equivariant Index Theorem on $\mathbb{R}^n$ in the Context of Continuous Fields of $C^*$-algebras. https://arxiv.org/abs/2401.07474

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