Singular subgroups in $\tilde{A}_2$-groups and their von Neumann algebras

Yongle Jiang; Piotr W. Nowak

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arXiv · 1811.03117

Singular subgroups in $\tilde{A}_2$-groups and their von Neumann algebras

Yongle Jiang·Piotr W. Nowak

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Abstract

We show that certain amenable subgroups inside $\tilde{A}_2$-groups are singular in the sense of Boutonnet and Carderi. This gives a new family of examples of singular group von Neumann subalgebras. We also give a geometric proof that if $G$ is an acylindrically hyperbolic group, $H$ is an infinite amenable subgroup containing a loxodromic element, then $H<G$ is singular. Finally, we present (counter)examples to show both situations happen concerning maximal amenability of $LH$ inside $LG$ if $H$ does not contain loxodromic elements.

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BibTeX RIS

Yongle Jiang, Piotr W. Nowak. 2018-11-07. Singular subgroups in $\tilde{A}_2$-groups and their von Neumann algebras. https://arxiv.org/abs/1811.03117

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