Realization of rigid C*-bicategories as bimodules over type II${}_1$ von Neumann algebras

Abstract

We prove that every rigid C*-bicategory with finite-dimensional centers (finitely decomposable horizontal units) can be realized as Connes' bimodules over finite direct sums of II${}_1$ factors. In particular, we realize every multitensor C*-category as bimodules over a finite direct sum of II${}_1$ factors.

arXiv comment21 pages

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Cited by in corpus (4)

• Haploid algebras in $C^{\ast }$-tensor categories and the Schellekens list
• A covariant Stinespring theorem
• Covariant quantum combinatorics with applications to zero-error communication
• Separable algebras in multitensor C${}^{\ast }$-categories are unitarizable