An example of an infinite amenable group with the ISR property

2023/12/13 by Jiang, Yongle, Zhou, Xiaoyan · 1 citation
#FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2312.08061

Abstract

Let G be S_ℕ, the finitary permutation (i.e. permutations with finite support) group on positive integers ℕ. We prove that G has the invariant von Neumann subalgebras rigidity (ISR, for short) property as introduced in Amrutam-Jiang's work. More precisely, every G-invariant von Neumann subalgebra P⊆ L(G) is of the form L(H) for some normal sugbroup H\lhd G and in this case, H=\e\, A_ℕ or G, where A_ℕ denotes the finitary alternating group on ℕ, i.e. the subgroup of all even permutations in S_ℕ. This gives the first known example of an infinite amenable group with the ISR property.

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