A Rigid Hyperfinite Type II1 Factor

Author:

Farah Ilijas1,Hirshberg Ilan2

Affiliation:

1. Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Ontario M3J 1P3, Canada

2. Department of Mathematics, Ben Gurion University of the Negev, P.O.B. 653, Be’er Sheva 84105, Israel

Abstract

Abstract We show that it is relatively consistent with Zermelo-Fraenkel set theory with the axiom of choice that there exists a hyperfinite type $\textrm{II}_1$-factor of density character $\aleph _1$ that is not isomorphic to its opposite, does not have any outer automorphisms, and has trivial fundamental group.

Funder

Israel Science Foundation

Fields Institute

National Science and Engineering Research Council

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Reference22 articles.

1. Consistency of a counterexample to Naimark’s problem;Akemann;Proc. Natl. Acad. Sci. U. S. A.,2004

2. An Introduction to II$_1$ Factors;Anantharaman

3. In Model Theory for Metric Structures;Ben Yaacov,2008

4. Invariant means and finite representation theory of ${\textit{C}}^{\ast } $-algebras;Brown;Mem. Amer. Math. Soc.,2006

5. Can you take Akemann–Weaver’s diamond away?;Calderón,2020

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Can you take Akemann–Weaver's 1 away?;Journal of Functional Analysis;2023-09

2. Nonseparable CCR algebras;International Journal of Mathematics;2021-09-30

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