2023/11/14 by David Kerr, Kerr, David, Spyridon Petrakos +1
Mathematics · Medicine · #Advanced Operator Algebra Research #Advanced Topology and Set Theory #Electroconvulsive Therapy Studies
paper · pdf · doi:10.48550/arxiv.2311.08192
Given a topologically free action of a countably infinite amenable group on the Cantor set, we prove that, for every subgroup G of the topological full group containing the alternating group, the group von Neumann algebra \mathscrL G is a McDuff factor. This yields the first examples of nonamenable simple finitely generated groups G for which \mathscrL G is McDuff. Using the same construction we show moreover that if a faithful action G\curvearrowright X of a countable group on a countable set with no finite orbits is amenable then the crossed product of the associated shift action over a given II1 factor is a McDuff factor. In particular, if H is a nontrivial countable ICC group and G\curvearrowright X is a faithful amenable action of a countable ICC group on a countable set with no finite orbits, then the group von Neumann algebra of the generalized wreath product H\wrX G is a McDuff factor. Our technique can also be applied to show that if H is a nontrivial countable group and G\curvearrowright X is an amenable action of a countable group on a countable set with no finite orbits then the generalized wreath product H\wrX G is Jones-Schmidt stable.