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, F (A^*n) =1, whenever 2≤ n <∞. This settles the non-separable version of the free group factor problem.