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Title: An exotic II$$_1$$ factor without property Gamma
We introduce a new iterative amalgamated free product construction of II factors, and use it to construct a separable II factor which does not have property Gamma and is not elementarily equivalent to the free group factor $$L(F_n)$$, for any $$n\geq 2$$. 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.  more » « less
Award ID(s):
2154637
PAR ID:
10509747
Author(s) / Creator(s):
; ;
Publisher / Repository:
Birkhauser
Date Published:
Journal Name:
Geometric and Functional Analysis
Volume:
33
Issue:
5
ISSN:
1016-443X
Page Range / eLocation ID:
1243 to 1265
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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