English

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 II1_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 II1_1 factors MM which do not admit tensor product decompositions M=PˉQM= P\bar \otimes Q into diffuse factors where QQ 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

R2 v1 2026-06-25T01:21:08.498Z