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Neretin groups admit no non-trivial invariant random subgroups

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arxiv 1905.07605 v1 pith:DM5R7NMH submitted 2019-05-18 math.GR

Tianyi Zheng This is my paper · ORCID
classification math.GR
keywords groupsinvariantneretinnon-trivialrandomsubgroupsadmitcompact
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We show that Neretin groups have no non-trivial invariant random subgroups. These groups provide first examples of non-discrete, compactly generated, locally compact groups with this property.

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Cited by 2 Pith papers

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  1. The regular representation of Neretin groups is factorial

    math.OA 2025-06 conditional novelty 8.0 of 10

    The regular representation of every Neretin group is factorial, yielding the first non-discrete simple group whose von Neumann algebra is a factor.

  2. Locally compact piecewise full groups of homeomorphisms

    math.GR 2025-01 conditional novelty 7.0 of 10

    Local decomposability characterises when a piecewise full group admits a unique non-discrete t.d.l.c. topology, and the resulting alternating full group is an open, compactly generated, simple derived subgroup that is...

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