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II$_1$ factors with exotic central sequence algebras

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arxiv 1904.06816 v1 pith:WQ2CMAGM submitted 2019-04-15 math.OA math.FA

Adrian Ioana , Pieter Spaas This is my paper · ORCID
classification math.OAmath.FA
keywords sequencealgebracentralfactorsalgebrasassociatedciteclass
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abstract

We provide a class of separable II$_1$ factors $M$ whose central sequence algebra is not the "tail" algebra associated to any decreasing sequence of von Neumann subalgebras of $M$. This settles a question of McDuff \cite{Mc69d}.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Stability for product groups and property $(\tau)$

    math.GR 2019-08 accept novelty 8.0 of 10

    Product groups Σ×Λ are not very flexibly P-stable when Σ admits a non-abelian free quotient and Λ lacks property (τ), so P-stability is not closed under direct products.

  2. Classification of tensor decompositions for II$_1$ factors

    math.OA 2019-08 conditional novelty 7.0 of 10

    For new classes of icc groups, every diffuse tensor decomposition of L(Γ) comes, up to conjugation and amplification, from a direct product decomposition of Γ.

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