Manifestly unitary higher Hilbert spaces
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866909338810974208 |
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| author | Chen, Quan Ferrer, Giovanni Hungar, Brett Penneys, David Sanford, Sean |
| author_facet | Chen, Quan Ferrer, Giovanni Hungar, Brett Penneys, David Sanford, Sean |
| contents | Higher idempotent completion gives a formal inductive construction of the $n$-category of finite dimensional $n$-vector spaces starting with the complex numbers. We propose a manifestly unitary construction of low dimensional higher Hilbert spaces, formally constructing the $\mathrm{C}^*$-3-category of 3-Hilbert spaces from Baez's 2-Hilbert spaces, which itself forms a 3-Hilbert space. We prove that the forgetful functor from 3-Hilbert spaces to 3-vector spaces is fully faithful. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_05120 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Manifestly unitary higher Hilbert spaces Chen, Quan Ferrer, Giovanni Hungar, Brett Penneys, David Sanford, Sean Quantum Algebra Category Theory Operator Algebras Primary: 18M40, 18N10, 18N20, Secondary: 18M20, 18M30, 18N25 Higher idempotent completion gives a formal inductive construction of the $n$-category of finite dimensional $n$-vector spaces starting with the complex numbers. We propose a manifestly unitary construction of low dimensional higher Hilbert spaces, formally constructing the $\mathrm{C}^*$-3-category of 3-Hilbert spaces from Baez's 2-Hilbert spaces, which itself forms a 3-Hilbert space. We prove that the forgetful functor from 3-Hilbert spaces to 3-vector spaces is fully faithful. |
| title | Manifestly unitary higher Hilbert spaces |
| topic | Quantum Algebra Category Theory Operator Algebras Primary: 18M40, 18N10, 18N20, Secondary: 18M20, 18M30, 18N25 |
| url | https://arxiv.org/abs/2410.05120 |