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

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.