Rank metric isometries and determinant-preserving mappings on II$_1$-factors
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908406443409408 |
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| author | Huang, Jinghao Kudaybergenov, Karimbergen Sukochev, Fedor |
| author_facet | Huang, Jinghao Kudaybergenov, Karimbergen Sukochev, Fedor |
| contents | We fully describe the general form of a linear (or conjugate-linear) rank metric isometry on the Murray--von Neumann algebra associated with a II$_1$-factor. As an application, we establish Frobenius' theorem in the setting of II$_1$-factors, by showing that every determinant-preserving linear bijection between two II$_1$-factors is necessarily an isomorphism or an anti-isomorphism. This confirms the Harris--Kadison conjecture (1996). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_11428 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rank metric isometries and determinant-preserving mappings on II$_1$-factors Huang, Jinghao Kudaybergenov, Karimbergen Sukochev, Fedor Operator Algebras 47L60, 47C15, 16E50 We fully describe the general form of a linear (or conjugate-linear) rank metric isometry on the Murray--von Neumann algebra associated with a II$_1$-factor. As an application, we establish Frobenius' theorem in the setting of II$_1$-factors, by showing that every determinant-preserving linear bijection between two II$_1$-factors is necessarily an isomorphism or an anti-isomorphism. This confirms the Harris--Kadison conjecture (1996). |
| title | Rank metric isometries and determinant-preserving mappings on II$_1$-factors |
| topic | Operator Algebras 47L60, 47C15, 16E50 |
| url | https://arxiv.org/abs/2506.11428 |