General solidity phenomena and anticoarse spaces for type $\mathrm{III}_1$ factors
Operator Algebras
2024-10-10 v2 Functional Analysis
Abstract
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 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.
Keywords
Cite
@article{arxiv.2409.18106,
title = {General solidity phenomena and anticoarse spaces for type $\mathrm{III}_1$ factors},
author = {Ben Hayes and David Jekel and Srivatsav Kunnawalkam Elayavalli and Brent Nelson},
journal= {arXiv preprint arXiv:2409.18106},
year = {2024}
}
Comments
33 pages. No figures. Added an appendix by Stefaan Vaes. Comments welcome!