| Title: |
General solidity phenomena and anticoarse spaces for type $\mathrm{III}_1$ factors |
| Authors: |
Hayes, Ben, Jekel, David, Elayavalli, Srivatsav Kunnawalkam, Nelson, Brent |
| Publication Year: |
2024 |
| Collection: |
Mathematics |
| Subject Terms: |
Mathematics - Operator Algebras, Mathematics - Functional Analysis |
| More Details: |
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.
Comment: 33 pages. No figures. Added an appendix by Stefaan Vaes. Comments welcome! |
| Document Type: |
Working Paper |
| Access URL: |
http://arxiv.org/abs/2409.18106 |
| Accession Number: |
edsarx.2409.18106 |
| Database: |
arXiv |
