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arXiv · 2212.11467

On unitary groups of crossed product von Neumann algebras

Yasuhito Hashiba
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Abstract

We consider the tracial crossed product algebra $M=A\rtimesΛ$ arising from a trace preserving action $σ:Λ\curvearrowright A$ of a discrete group $Λ$ on a tracial von Neumann algebra $A$. For a unitary subgroup $\mathcal{G}\subset \mathcal{U}(M)$, we study when this $\mathcal{G}$ can be conjugated into $\mathcal{U}(A)\cdotΛ$ in $M$. We provide a general sufficient condition for this to happen. Our result generalizes a result of Ioana, Popa and Vaes, which treats the case when $M$ is the group von Neumann algebra $L(Λ)$.

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Yasuhito Hashiba. 2022-12-22. On unitary groups of crossed product von Neumann algebras. https://arxiv.org/abs/2212.11467

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