Spectral dimension of $p$-adic integers
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911017143894016 |
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| author | Biswas, Surajit Saurabh, Bipul |
| author_facet | Biswas, Surajit Saurabh, Bipul |
| contents | The notion of spectral dimension was introduced by Chakraborty and Pal in \cite{cp}. In this paper, we show that the spectral dimension of the ring of $p$-adic integers, $\mathbb{Z}_p$, is equal to its manifold dimension, which is $0$. Finally, we determine the $K$-groups of $\mathbb{Z}_p$, and show that the generators of $K_0(\mathbb{Z}_p)$ can be expressed as finite span of the characters of $\mathbb{Z}_p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_18890 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spectral dimension of $p$-adic integers Biswas, Surajit Saurabh, Bipul Quantum Algebra 46L87 The notion of spectral dimension was introduced by Chakraborty and Pal in \cite{cp}. In this paper, we show that the spectral dimension of the ring of $p$-adic integers, $\mathbb{Z}_p$, is equal to its manifold dimension, which is $0$. Finally, we determine the $K$-groups of $\mathbb{Z}_p$, and show that the generators of $K_0(\mathbb{Z}_p)$ can be expressed as finite span of the characters of $\mathbb{Z}_p$. |
| title | Spectral dimension of $p$-adic integers |
| topic | Quantum Algebra 46L87 |
| url | https://arxiv.org/abs/2406.18890 |