Prime II1 factors arising from actions of product groups

Daniel Drimbe

doi:10.48550/arxiv.1904.06637

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Prime II1 factors arising from actions of product groups

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Open access

Prime II1 factors arising from actions of product groups

Daniel Drimbe

ArXiv.org

Cornell University

04/14/2019

DOI: 10.48550/arxiv.1904.06637

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Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

We prove that any II1 factor arising from a free ergodic probability measure preserving action Γ↷X of a product Γ=Γ1×⋯×Γn of icc hyperbolic, free product or wreath product groups is prime, provided Γi↷X is ergodic, for any 1≤i≤n. We also completely classify all the tensor product decompositions of a II1 factor associated to a free ergodic probability measure preserving action of a product of icc, hyperbolic, property (T) groups. As a consequence, we derive a unique prime factorization result for such II1 factors. Finally, we obtain a unique prime factorization theorem for a large class of II1 factors which have property Gamma.

Mathematics - Dynamical Systems

Mathematics - Functional Analysis

Mathematics - Operator Algebras

Details

Title: Subtitle: Prime II1 factors arising from actions of product groups
Creators: Daniel Drimbe
Resource Type: Preprint
Publication Details: ArXiv.org
Publisher: Cornell University; Ithaca, New York
DOI: 10.48550/arxiv.1904.06637
ISSN: 2331-8422
Language: English
Date posted: 04/14/2019
Academic Unit: Mathematics
Record Identifier: 9984696834802771

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