An exotic II₁ factor without property Gamma

2022/09/21 by Chifan, Ionut, Ioana, Adrian, Elayavalli, Srivatsav Kunnawalkam
#FOS: Mathematics #Functional Analysis (math.FA) #Logic (math.LO) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2209.10645

Abstract

We introduce a new iterative amalgamated free product construction of II₁ factors, and use it to construct a separable II₁ factor which does not have property Gamma and is not elementarily equivalent to the free group factor L(\mathbb F_n), for any 2≤ n≤ ∞. This provides the first explicit example of two non-elementarily equivalent II₁ factors without property Gamma. Moreover, our construction also provides the first explicit example of a II₁ 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.

Related

• 3-handle construction on II₁ factors
• Strongly solid \rm II₁ factors with an exotic MASA
• Singly Generated II₁ Factors
• On a Subfactor Construction of a Factor Non Anti-Isomorphic to Itself
• Two applications of free entropy