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arXiv · 2409.18106

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

Ben Hayes·David Jekel·Srivatsav Kunnawalkam Elayavalli·Brent Nelson
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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 $\mathrm{III}$ 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.

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Ben Hayes, David Jekel, Srivatsav Kunnawalkam Elayavalli, Brent Nelson. 2024-09-26. General solidity phenomena and anticoarse spaces for type $\mathrm{III}_1$ factors. https://arxiv.org/abs/2409.18106

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