Duke Mathematical Journal

II1 factors with nonisomorphic ultrapowers

Rémi Boutonnet, Ionuţ Chifan, and Adrian Ioana

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Abstract

We prove that there exist uncountably many separable II1 factors whose ultrapowers (with respect to arbitrary ultrafilters) are nonisomorphic. In fact, we prove that the families of nonisomorphic II1 factors originally introduced by McDuff are such examples. This entails the existence of a continuum of nonelementarily equivalent II1 factors, thus settling a well-known open problem in the continuous model theory of operator algebras.

Article information

Source
Duke Math. J., Volume 166, Number 11 (2017), 2023-2051.

Dates
Received: 29 July 2016
Revised: 16 November 2016
First available in Project Euclid: 28 March 2017

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1490666575

Digital Object Identifier
doi:10.1215/00127094-0000017X

Mathematical Reviews number (MathSciNet)
MR3694564

Zentralblatt MATH identifier
1384.46040

Subjects
Primary: 46L10: General theory of von Neumann algebras
Secondary: 03C20: Ultraproducts and related constructions

Keywords
II$_{1}$ factor von Neumann algebras central sequence ultrapower ultraproduct continuous model theory

Citation

Boutonnet, Rémi; Chifan, Ionuţ; Ioana, Adrian. II $_{1}$ factors with nonisomorphic ultrapowers. Duke Math. J. 166 (2017), no. 11, 2023--2051. doi:10.1215/00127094-0000017X. https://projecteuclid.org/euclid.dmj/1490666575


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