Realizations of Rigid C*-Tensor Categories as Bimodules over GJS C*-Algebras

TL;DR

This paper constructs explicit realizations of rigid C*-tensor categories as bimodules over specific GJS C*-algebras, linking abstract categorical structures to concrete operator algebra frameworks.

Contribution

It introduces a new functorial realization of rigid C*-tensor categories as bimodules over GJS C*-algebras, extending previous theoretical work with explicit constructions.

Findings

Constructs a fully-faithful functor from the category to bimodules over GJS C*-algebras.

Establishes a functor into bimodules over interpolated free group factors.

Recovers a previously known functor through a composition of the new functors.

Abstract

Given an arbitrary countably generated rigid C*-tensor category, we construct a fully-faithful bi-involutive strong monoidal functor onto a subcategory of finitely generated projective bimodules over a simple, exact, separable, unital C*-algebra with unique trace. The C*-algebras involved are built from the category using the GJS-construction introduced in arXiv:0911.4728 and further studied in arXiv:1208.5505 and arXiv:1401.2486. Out of this category of Hilbert C*-bimodules, we construct a fully-faithful bi-involutive strong monoidal functor into the category of bi-finite spherical bimodules over an interpolated free group factor. The composite of these two functors recovers the functor constructed in arXiv:1208.5505