Tensor product decompositions and rigidity of full factors

2019/05/24 by Yusuke Isono, Isono, Yusuke, Amine Marrakchi +1 · 3 citations
Mathematics · #46L10 #46L36 #46L40 #46L55 #Advanced Operator Algebra Research #Advanced Topology and Set Theory #FOS: Mathematics #Operator Algebras (math.OA) #Rings, Modules, and Algebras

paper · doi:10.48550/arxiv.1905.09974

openalex publication_date 2019/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 coming from compact actions of higher rank lattices (e.g. SL(n,ℤ), n ≥ 3) and noncommutative Bernoulli shifts with arbitrary base (not necessarily amenable). Finally, we provide examples of full factors without any prime factorization.

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