2019
DOI: 10.48550/arxiv.1905.09974
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Tensor product decompositions and rigidity of full factors

Abstract: We obtain several rigidity results regarding tensor product decompositions of factors. First, we show that any full factor with separable predual has at most countably many tensor product decompositions up to stable unitary conjugacy. We use this to show that the class of separable full factors with countable fundamental group is stable under tensor products. Next, we obtain new primeness and unique prime factorization results for crossed products comming from compact actions of higher rank lattices (e.g. SL(n… Show more

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“…• Tensor product factors P ⊗ Q, where P is a type III 1 factor with trivial bicentralizer and Q is any factor [Ma18] (see also [IM19,Lemma 7.5]).…”
Section: Introductionmentioning
confidence: 99%
“…• Tensor product factors P ⊗ Q, where P is a type III 1 factor with trivial bicentralizer and Q is any factor [Ma18] (see also [IM19,Lemma 7.5]).…”
Section: Introductionmentioning
confidence: 99%