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Locally compact groups acting on trees, the type I conjecture and non-amenable von Neumann algebras
Stockholm University, Faculty of Science, Department of Mathematics.
Number of Authors: 22019 (English)In: Commentarii Mathematici Helvetici, ISSN 0010-2571, E-ISSN 1420-8946, Vol. 94, no 1, p. 185-219Article in journal (Refereed) Published
Abstract [en]

We address the problem to characterise closed type I subgroups of the automorphism group of a tree. Even in the well-studied case of Burger-Mozes' universal groups, non-type I criteria were unknown. We prove that a huge class of groups acting properly on trees are not of type I. In the case of Burger-Mozes groups, this yields a complete classification of type I groups among them. Our key novelty is the use of von Neumann algebraic techniques to prove the stronger statement that the group von Neumann algebra of the groups under consideration is non-amenable.

Place, publisher, year, edition, pages
2019. Vol. 94, no 1, p. 185-219
Keywords [en]
Groups acting on trees, type I groups, free product von Neumann algebras
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-167691DOI: 10.4171/CMH/458ISI: 000460420600007OAI: oai:DiVA.org:su-167691DiVA, id: diva2:1301389
Available from: 2019-04-01 Created: 2019-04-01 Last updated: 2019-04-01Bibliographically approved

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