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- Title
An example of an infinite amenable group with the ISR property.
- Authors
Jiang, Yongle; Zhou, Xiaoyan
- Abstract
Let G be S N , the finitary permutation (i.e., permutations with finite support) group on the set of 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 subgroup H ⊲ 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.
- Subjects
VON Neumann algebras; INFINITE groups; PERMUTATIONS; PERMUTATION groups; INTEGERS
- Publication
Mathematische Zeitschrift, 2024, Vol 307, Issue 2, p1
- ISSN
0025-5874
- Publication type
Article
- DOI
10.1007/s00209-024-03495-8