Tensor product indecomposability results for existentially closed factors
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 factors. Using a m\'elange of techniques from deformation/rigidity theory, model theory, and the recent works CIOS21,CDI22 we highlight an uncountable family of existentially closed II1 factors M which do not admit tensor product decompositions M= P 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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