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

Proceedings of the American Mathematical Society, Series B Pub Date : 2022-01-18 DOI:10.1090/bproc/133

Ryoya Arimoto

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引用次数: 2

Abstract

The Neretin group N d , k \mathcal {N}_{d, k} is the totally disconnected locally compact group consisting of almost automorphisms of the tree T d , k \mathcal {T}_{d, k} . This group has a distinguished open subgroup O d , k \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 O d , k \mathcal {O}_{d, k} is of type I or not.

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关于Neretin群的一个开子群的von Neumann代数的类型

Neretin群N d, k \mathcal {N}_{d, k}是由树T d, k \mathcal {T}_{d, k}的几乎自同构组成的完全不连通的局部紧群。这个群有一个开放的子群O d, k \mathcal {O}_{d, k}。我们证明了这个开放子群不是i型的，给出了p - e最近结果的另一种证明。Caprace, A. Le Boudec和N. Matte Bon指出Neretin群不是I型，并回答了他们的问题O d, k \mathcal {O}_{d, k}是否属于I型。

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来源期刊

Proceedings of the American Mathematical Society, Series B

CiteScore

1.60

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0.00%

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