Tensor product indecomposability results for existentially closed factors
Operator Algebras
2022-08-02 v1 Group Theory
Logic
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 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 factors which do not admit tensor product decompositions into diffuse factors where is full. In the last section we discuss several open problems regarding the structural theory of existentially closed factors.
Keywords
Cite
@article{arxiv.2208.00259,
title = {Tensor product indecomposability results for existentially closed factors},
author = {Ionut Chifan and Daniel Drimbe and Adrian Ioana},
journal= {arXiv preprint arXiv:2208.00259},
year = {2022}
}
Comments
28 pages, submitted to a volume on Model Theory of Operator Algebras that will be published in the De Gruyter series Logic and its Applications