Transfinite Extension of Nuclear Dimension
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929375807537152 |
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| author | Zhu, Jingming Zhang, Jiawen |
| author_facet | Zhu, Jingming Zhang, Jiawen |
| contents | In this paper, we introduce a notion of transfinite nuclear dimension for $C^*$-algebras, which coincides with the nuclear dimension when taking values in natural numbers. We use it to characterise a stronger form of having nuclear dimension at most $ω$ and moreover, we show that the transfinite nuclear dimension of a uniform Roe algebra is bounded by the transfinite asymptotic dimension of the underlying space. Hence we obtain that the uniform Roe algebra for spaces with asymptotic property C has the corona factorisation property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_16335 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Transfinite Extension of Nuclear Dimension Zhu, Jingming Zhang, Jiawen Operator Algebras In this paper, we introduce a notion of transfinite nuclear dimension for $C^*$-algebras, which coincides with the nuclear dimension when taking values in natural numbers. We use it to characterise a stronger form of having nuclear dimension at most $ω$ and moreover, we show that the transfinite nuclear dimension of a uniform Roe algebra is bounded by the transfinite asymptotic dimension of the underlying space. Hence we obtain that the uniform Roe algebra for spaces with asymptotic property C has the corona factorisation property. |
| title | Transfinite Extension of Nuclear Dimension |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2402.16335 |