An exotic II1 factor without property Gamma

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 L ( F n ) , for any 2 ≤ n ≤ ∞ . This provides the first explicit example...

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Bibliographic Details
Published inGeometric and functional analysis Vol. 33; no. 5; pp. 1243 - 1265
Main Authors Chifan, Ionuţ, Ioana, Adrian, Kunnawalkam Elayavalli, Srivatsav
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.10.2023
Springer Nature B.V
Subjects
Analysis
Equivalence
Mathematics
Mathematics and Statistics
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Summary: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 L ( F n ) , for any 2 ≤ n ≤ ∞ . 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.
Bibliography:ObjectType-Article-1
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ISSN:1016-443X
1420-8970
DOI:10.1007/s00039-023-00649-4