Non-isomorphism of A^*n, 2≤ n ≤ ∞, for a non-separable abelian von Neumann algebra A

2023/08/10 by Boutonnet, Rémi, Drimbe, Daniel, Ioana, Adrian +1
#FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2308.05671

Abstract

We prove that if A is a non-separable abelian tracial von Neuman algebra then its free powers A^*n, 2≤ n ≤ ∞, are mutually non-isomorphic and with trivial fundamental group, \mathcal F(A^*n)=1, whenever 2≤ n<∞. This settles the non-separable version of the free group factor problem.

Related

• L²-rigidity in von Neumann algebras
• Free products and rescalings involving non-separable abelian von Neumann algebras
• Unsolvability of the isomorphism problem for [free abelian]-by-free groups
• Indecomposability of free group factors over nonprime subfactors and abelian subalgebras
• Embedding universality for II₁ factors with property (T)