Quantum Expanders and Quantifier Reduction for Tracial von Neumann Algebras
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911043010166784 |
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| author | Farah, Ilijas Jekel, David Pi, Jennifer |
| author_facet | Farah, Ilijas Jekel, David Pi, Jennifer |
| contents | We provide a complete characterization of theories of tracial von Neumann algebras that admit quantifier elimination. We also show that the theory of a separable tracial von Neumann algebra $\mathcal{N}$ is never model complete if its direct integral decomposition contains $\mathrm{II}_1$ factors $\mathcal{M}$ such that $M_2(\mathcal{M})$ embeds into an ultrapower of $\mathcal{M}$. The proof in the case of $\mathrm{II}_1$ factors uses an explicit construction based on random matrices and quantum expanders. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_06197 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quantum Expanders and Quantifier Reduction for Tracial von Neumann Algebras Farah, Ilijas Jekel, David Pi, Jennifer Operator Algebras Logic We provide a complete characterization of theories of tracial von Neumann algebras that admit quantifier elimination. We also show that the theory of a separable tracial von Neumann algebra $\mathcal{N}$ is never model complete if its direct integral decomposition contains $\mathrm{II}_1$ factors $\mathcal{M}$ such that $M_2(\mathcal{M})$ embeds into an ultrapower of $\mathcal{M}$. The proof in the case of $\mathrm{II}_1$ factors uses an explicit construction based on random matrices and quantum expanders. |
| title | Quantum Expanders and Quantifier Reduction for Tracial von Neumann Algebras |
| topic | Operator Algebras Logic |
| url | https://arxiv.org/abs/2310.06197 |