The regular representation of every Neretin group is factorial, yielding the first non-discrete simple group whose von Neumann algebra is a factor.
Neretin groups admit no non-trivial invariant random subgroups
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abstract
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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The regular representation of Neretin groups is factorial
The regular representation of every Neretin group is factorial, yielding the first non-discrete simple group whose von Neumann algebra is a factor.