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arXiv · 2208.00259

Tensor product indecomposability results for existentially closed factors

Ionut Chifan·Daniel Drimbe·Adrian Ioana
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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.

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Ionut Chifan, Daniel Drimbe, Adrian Ioana. 2022-07-30. Tensor product indecomposability results for existentially closed factors. https://arxiv.org/abs/2208.00259

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