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Co-amenability and Connes’s embedding problem

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Abstract

A longstanding open question of Connes asks whether any finite von Neumann algebra embeds into an ultraproduct of finite-dimensional matrix algebras. As of yet, algebras verified to satisfy the Connes’s embedding property belong to just a few special classes (e.g., amenable algebras and free group factors). In this article, we prove that von Neumann algebras satisfying Popa’s co-amenability have Connes’s embedding property.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of New Hampshire, Durham, NH, 03824, USA

    JinSong Wu

  2. School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, China

    JinSong Wu

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  1. JinSong Wu
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Correspondence to JinSong Wu.

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Wu, J. Co-amenability and Connes’s embedding problem. Sci. China Math. 55, 977–984 (2012). https://doi.org/10.1007/s11425-012-4369-z

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  • DOI: https://doi.org/10.1007/s11425-012-4369-z

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