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arXiv · 2201.06840

On the type of the von Neumann algebra of an open subgroup of the Neretin group

Ryoya Arimoto
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Abstract

The Neretin group $\mathcal{N}_{d,k}$ is the totally disconnected locally compact group consisting of almost automorphisms of the tree $\mathcal{T}_{d,k}$. This group has a distinguished open subgroup $\mathcal{O}_{d,k}$. We prove that this open subgroup is not of type I. This gives an alternative proof of the recent result of P.-E. Caprace, A. Le Boudec and N. Matte Bon which states that the Neretin group is not of type I, and answers their question whether $\mathcal{O}_{d,k}$ is of type I or not.

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Ryoya Arimoto. 2022-01-18. On the type of the von Neumann algebra of an open subgroup of the Neretin group. https://arxiv.org/abs/2201.06840

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