General solidity phenomena and anticoarse spaces for type $\mathrm{III}_1$ factors
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866908079082176512 |
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| author | Hayes, Ben Jekel, David Elayavalli, Srivatsav Kunnawalkam Nelson, Brent |
| author_facet | Hayes, Ben Jekel, David Elayavalli, Srivatsav Kunnawalkam Nelson, Brent |
| contents | By developing a theory of anticoarse spaces in the purely infinite setting and using 1-bounded entropy techniques along with recent strong convergence results in random matrix theory, we show that free Araki--Woods factors offer the first examples of type $\mathrm{III}$ factors satisfying vastly general degrees of indecomposability phenomena. Notably this includes strong solidity with respect to any weakening of the normalizer currently in the literature and the Peterson--Thom property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_18106 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | General solidity phenomena and anticoarse spaces for type $\mathrm{III}_1$ factors Hayes, Ben Jekel, David Elayavalli, Srivatsav Kunnawalkam Nelson, Brent Operator Algebras Functional Analysis By developing a theory of anticoarse spaces in the purely infinite setting and using 1-bounded entropy techniques along with recent strong convergence results in random matrix theory, we show that free Araki--Woods factors offer the first examples of type $\mathrm{III}$ factors satisfying vastly general degrees of indecomposability phenomena. Notably this includes strong solidity with respect to any weakening of the normalizer currently in the literature and the Peterson--Thom property. |
| title | General solidity phenomena and anticoarse spaces for type $\mathrm{III}_1$ factors |
| topic | Operator Algebras Functional Analysis |
| url | https://arxiv.org/abs/2409.18106 |