Equivariant Index Theorem on $\mathbb{R}^n$ in the Context of Continuous Fields of $C^*$-algebras
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866913196684607488 |
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| author | Ren, Baiying Wang, Hang Wang, Zijing |
| author_facet | Ren, Baiying Wang, Hang Wang, Zijing |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_07474 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Equivariant Index Theorem on $\mathbb{R}^n$ in the Context of Continuous Fields of $C^*$-algebras Ren, Baiying Wang, Hang Wang, Zijing Operator Algebras Differential Geometry 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. |
| title | Equivariant Index Theorem on $\mathbb{R}^n$ in the Context of Continuous Fields of $C^*$-algebras |
| topic | Operator Algebras Differential Geometry |
| url | https://arxiv.org/abs/2401.07474 |