Tensor product indecomposability results for existentially closed factors

Autor:	Chifan, Ionut, Drimbe, Daniel, Ioana, Adrian
Rok vydání:	2022
Předmět:	Mathematics - Operator Algebras Mathematics - Group Theory Mathematics - Logic
Druh dokumentu:	Working Paper
Popis:	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. Comment: 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
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2208.00259 Zobrazit plný text záznamu View this record from Arxiv