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Non-isomorphism of $A^{*n}, 2\leq n \leq \infty$, for a non-separable abelian von Neumann algebra $A$

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arxiv 2308.05671 v1 pith:MAX7N5UQ submitted 2023-08-10 math.OA math.FA

Rémi Boutonnet , Daniel Drimbe , Adrian Ioana , Sorin Popa This is my paper · ORCID
classification math.OAmath.FA
keywords inftynon-separableabelianalgebrafreegroupfactorfundamental
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abstract

We prove that if $A$ is a non-separable abelian tracial von Neuman algebra then its free powers $A^{*n}, 2\leq n \leq \infty$, are mutually non-isomorphic and with trivial fundamental group, $\mathcal F(A^{*n})=1$, whenever $2\leq n<\infty$. This settles the non-separable version of the free group factor problem.

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  1. Compressible subalgebras in II$_1$ factors

    math.OA 2025-10 conditional novelty 7.0 of 10

    Compressible subalgebras of II1 factors force every AFD subalgebra's Hilbert bimodule to contain a coarse bimodule, blocking tight complements and AFD-ergodicity.

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