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

Michael Hartglass; Roberto Hernandez Palomares

doi:10.1063/5.0015294

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

Operator Algebras 2026-01-06 v1 Quantum Algebra

Authors: Michael Hartglass , Roberto Hernandez Palomares

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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

Keywords

rigid c*-tensor category gjs c*-algebra hilbert c*-bimodules strong monoidal functor interpolated free group factor spherical bimodules

Cite

@article{arxiv.2005.09821,
  title  = {Realizations of Rigid C*-Tensor Categories as Bimodules over GJS C*-Algebras},
  author = {Michael Hartglass and Roberto Hernandez Palomares},
  journal= {arXiv preprint arXiv:2005.09821},
  year   = {2026}
}

Comments

32 pages, many figures