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

Remi Boutonnet; Daniel Drimbe; Adrian Ioana; Sorin Popa

doi:10.1007/s00039-024-00669-8

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

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

Remi Boutonnet, Daniel Drimbe, Adrian Ioana and Sorin Popa

Geometric and functional analysis, Vol.34(2), pp.393-408

04/01/2024

DOI: 10.1007/s00039-024-00669-8

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Abstract

We prove that if A is a non-separable abelian tracial von Neuman algebra then its free powers A(& lowast;n), 2 <= n <= infinity, are mutually non-isomorphic and with trivial fundamental group, F(A(& lowast;n)) = 1, whenever 2 <= n < infinity. This settles the non-separableversion of the free group factor problem

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Title: Subtitle: Non-isomorphism of A∗n,2 ≤ n ≤ ∞, for a non-separable abelian von Neumann algebra A
Creators: Remi Boutonnet - Institut de Mathématiques de Bordeaux
Daniel Drimbe - University of Oxford
Adrian Ioana - University of California, San Diego
Sorin Popa - University of California, Los Angeles
Resource Type: Journal article
Publication Details: Geometric and functional analysis, Vol.34(2), pp.393-408
Publisher: Springer Nature
DOI: 10.1007/s00039-024-00669-8
ISSN: 1016-443X
eISSN: 1420-8970
Number of pages: 16
Grant note: 19-CE40-0008 / ANR; Agence Nationale de la Recherche (ANR) Takesaki Endowed Chairat UCLA Simons Fellowship 1854074; 2153805; DMS-1955812 / NSF; National Science Foundation (NSF) 12T5221N / Research Foundation Flanders; FWO
Language: English
Date published: 04/01/2024
Academic Unit: Mathematics
Record Identifier: 9984696753302771

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