A remark about the Connes fusion tensor product
Operator Algebras
2007-05-23 v1
Abstract
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 .
Cite
@article{arxiv.math/0601045,
title = {A remark about the Connes fusion tensor product},
author = {Andreas Thom},
journal= {arXiv preprint arXiv:math/0601045},
year = {2007}
}