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

Arimoto, Ryoya

doi:10.1090/bproc/133

On the type of the von Neumann algebra of an open subgroup of the Neretin group
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by Ryoya Arimoto HTML | PDF

Proc. Amer. Math. Soc. Ser. B 9 (2022), 311-316

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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