On the type of the von Neumann algebra of an open subgroup of the Neretin group-Reference-Cited by-同舟云学术

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

Published:2022-07-07 Issue:29 Volume:9 Page:311-316
ISSN:2330-1511
Container-title:Proceedings of the American Mathematical Society, Series B
language:en
Short-container-title:Proc. Amer. Math. Soc. Ser. B

Author:

Arimoto Ryoya

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.

Publisher

American Mathematical Society (AMS)

Subject

Geometry and Topology,Discrete Mathematics and Combinatorics,Analysis,Algebra and Number Theory

Link

https://www.ams.org/bproc/2022-09-29/S2330-1511-2022-00133-0/S2330-1511-2022-00133-0.pdf

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