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Unique prime factorization for infinite tensor product factors

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arxiv 1712.00925 v2 pith:T5JHN3KA submitted 2017-12-04 math.OA

Yusuke Isono This is my paper · ORCID
classification math.OA
keywords factorsproductinfinitetensorfactorizationfreeprimeproperty
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In this article, we investigate a unique prime factorization property for infinite tensor product factors. We provide several examples of type II and III factors which satisfy this property, including all free product factors with diffuse free product components. In the type III setting, this is the first classification result for infinite tensor product non-amenable factors. Our proof is based on Popa's intertwining techniques and a characterization of relative amenability on the continuous cores.

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