2006/01/03 by Andreas Thom, Thom, Andreas
Mathematics · #46L #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Operator Algebras (math.OA) #math.OA #msc:46L
paper · pdf · doi:10.48550/arxiv.math/0601045
arxiv created 2006/01/03 · openalex publication_date 2006/01/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We analyze the algebraic structure of the Connes fusion tensor product (CFTP) in the case of bi-finite Hilbert modules over a von Neumann algebra M. It turns out that all complications in its definition disappear if one uses the closely related bi-modules of bounded vectors. We construct an equivalence of monoidal categories with duality between a category of Hilbert bi-modules over M with CFTP and some natural category of bi-modules over M with the usual relative algebraic tensor product. The results are surely well-known to the experts. We hope that the exposition and presentation is useful for those who want to learn about the CFTP .