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, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\mathcal{F}(A^{*n})=1$\\end{document}, whenever 2≤n<∞. This settles the non-separable version of the free group factor problem.