Two non-elementarily equivalent II$_1$ factors without property Gamma

Ionuţ Chifan; Adrian Ioana; Srivatsav Kunnawalkam Elayavalli

doi:10.48550/arXiv.2209.10645

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Two non-elementarily equivalent II$_1$ factors without property Gamma

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Two non-elementarily equivalent II$_1$ factors without property Gamma

Ionuţ Chifan, Adrian Ioana and Srivatsav Kunnawalkam Elayavalli

ArXiv.org

09/21/2022

DOI: 10.48550/arXiv.2209.10645

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Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

We introduce a new iterative amalgamated free product construction of II$_1$ factors, and use it to construct a separable II$_1$ factor which does not have property Gamma and is not elementarily equivalent to the free group factor $\text{L}(\mathbb F_n)$, for any $2\leq n\leq \infty$. This provides the first explicit example of two non-elementarily equivalent II$_1$ factors without property Gamma. Moreover, our construction also provides the first explicit example of a II$_1$ factor without property Gamma that is also not elementarily equivalent to any ultraproduct of matrix algebras. Our proofs use a blend of techniques from Voiculescu's free entropy theory and Popa's deformation/rigidity theory.

Details

Title: Subtitle: Two non-elementarily equivalent II$_1$ factors without property Gamma
Creators: Ionuţ Chifan
Adrian Ioana
Srivatsav Kunnawalkam Elayavalli
Resource Type: Preprint
Publication Details: ArXiv.org
DOI: 10.48550/arXiv.2209.10645
ISSN: 2331-8422
Language: English
Date posted: 09/21/2022
Academic Unit: Mathematics
Record Identifier: 9984297558802771

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