Tensor product indecomposability results for existentially closed factors

Ionut Chifan; Daniel Drimbe; Adrian Ioana

doi:10.48550/arXiv.2208.00259

Back

Tensor product indecomposability results for existentially closed factors

Preprint

Open access

Tensor product indecomposability results for existentially closed factors

Ionut Chifan, Daniel Drimbe and Adrian Ioana

ArXiv.org

07/30/2022

DOI: 10.48550/arXiv.2208.00259

Files and links (1)

url

https://doi.org/10.48550/arXiv.2208.00259View

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

In the first part of the paper we survey several results from Popa's deformation/rigidity theory on the classification of tensor product decompositions of large natural classes of II$_1$ factors. Using a m\'elange of techniques from deformation/rigidity theory, model theory, and the recent works \cite{CIOS21,CDI22} we highlight an uncountable family of existentially closed II$_1$ factors $M$ which do not admit tensor product decompositions $M= P\bar \otimes Q$ into diffuse factors where $Q$ is full. In the last section we discuss several open problems regarding the structural theory of existentially closed factors.

Details

Title: Subtitle: Tensor product indecomposability results for existentially closed factors
Creators: Ionut Chifan
Daniel Drimbe
Adrian Ioana
Resource Type: Preprint
Publication Details: ArXiv.org
DOI: 10.48550/arXiv.2208.00259
ISSN: 2331-8422
Language: English
Date posted: 07/30/2022
Academic Unit: Mathematics
Record Identifier: 9984277654002771

Metrics

31 Record Views