There is no separable universal $\mathrm {II}_1$-factor
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- by Narutaka Ozawa PDF
- Proc. Amer. Math. Soc. 132 (2004), 487-490 Request permission
Abstract:
Gromov constructed uncountably many pairwise nonisomorphic discrete groups with Kazhdan’s property $\mathrm {(T)}$. We will show that no separable $\mathrm {II}_1$-factor can contain all these groups in its unitary group. In particular, no separable $\mathrm {II}_1$-factor can contain all separable $\mathrm {II}_1$-factors in it. We also show that the full group $C^*$-algebras of some of these groups fail the lifting property.References
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Additional Information
- Narutaka Ozawa
- Affiliation: Department of Mathematical Science, University of Tokyo, Tokyo 153-8914, Japan
- Email: narutaka@ms.u-tokyo.ac.jp
- Received by editor(s): October 10, 2002
- Published electronically: June 23, 2003
- Additional Notes: The author was partially supported by JSPS Postdoctoral Fellowships for Research Abroad.
- Communicated by: David R. Larson
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 487-490
- MSC (2000): Primary 46L10; Secondary 20F65
- DOI: https://doi.org/10.1090/S0002-9939-03-07127-2
- MathSciNet review: 2022373