论文标题
关于NERETIN组的开放子组的von Neumann代数的类型
On the type of the von Neumann algebra of an open subgroup of the Neretin group
论文作者
论文摘要
NERETIN组$ \ MATHCAL {N} _ {D，K} $是完全断开的本地紧凑组，该组几乎由树$ \ Mathcal {T} _ {D，K} $组成。该组有一个杰出的开放子组$ \ MATHCAL {O} _ {D，K} $。我们证明，此开放子组不是类型I的。这给出了P.-E的最新结果的替代证明。 Caprace，A。LeBoudec和N. Matte Bon，指出NERETIN组不是I型，并回答了他们的问题，是否$ \ Mathcal {O} _ {d，K} $是I类型I类型。
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.
