The noncommutative geometry of frame bundles
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866915691792171008 |
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| author | Wagner, Stefan |
| author_facet | Wagner, Stefan |
| contents | We apply ourselves to the noncommutative geometry of frame bundles by showing that each C$^*$-algebraic noncommutative principal $\mathrm{SO}(n)$-bundle is, up to isomorphism, uniquely determined by its associated noncommutative vector bundle with respect to the standard representation of $\mathrm{SO}(n)$. For this, we provide a construction procedure, via unitary tensor functors, that for a certain type of correspondence, let's say $M$, attaches a free C$^*$-dynamical system $(\mathcal{A}_M,\mathrm{SO}(n),α_M)$ with the property that its associated noncommutative vector bundle with respect to the standard representation of $\mathrm{SO}(n)$ is isomorphic to $M$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_14010 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The noncommutative geometry of frame bundles Wagner, Stefan Operator Algebras Mathematical Physics Differential Geometry 58B34, 46L87 (primary), 55R10 (secondary) We apply ourselves to the noncommutative geometry of frame bundles by showing that each C$^*$-algebraic noncommutative principal $\mathrm{SO}(n)$-bundle is, up to isomorphism, uniquely determined by its associated noncommutative vector bundle with respect to the standard representation of $\mathrm{SO}(n)$. For this, we provide a construction procedure, via unitary tensor functors, that for a certain type of correspondence, let's say $M$, attaches a free C$^*$-dynamical system $(\mathcal{A}_M,\mathrm{SO}(n),α_M)$ with the property that its associated noncommutative vector bundle with respect to the standard representation of $\mathrm{SO}(n)$ is isomorphic to $M$. |
| title | The noncommutative geometry of frame bundles |
| topic | Operator Algebras Mathematical Physics Differential Geometry 58B34, 46L87 (primary), 55R10 (secondary) |
| url | https://arxiv.org/abs/2304.14010 |