paper

General solidity phenomena and anticoarse spaces for type factors

arXiv:2409.18106

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.

33 pages. No figures. Added an appendix by Stefaan Vaes. Comments welcome!

General solidity phenomena and anticoarse spaces for type $\mathrm{III}_1$ factors · wovepaper