OP-01002 Open

Biexactness of the bidual of the reduced C*-algebra of F₂

Biexactness here is Ding and Peterson's notion for von Neumann algebras.

Problem. Is the von Neumann algebra $(C^*_r\mathbb F_2)^{**}$ biexact?

Source: Credited to C. Ding and J. Peterson (2023), who introduced biexactness for von Neumann algebras; listed as F.4 in J. Peterson, Open problems in operator algebras (version of 15 May 2026).

Imported from math.uwaterloo.ca/~j37peter/problems.html.

Classification

Primary: OA — Operator Algebras
Keywords: biexactness, enveloping von Neumann algebras, Peterson's operator algebra problems, reduced group C*-algebras
Literature checked: Oct. 26, 2026 by clemens-admin

References

@misc{ding2023,
  author        = {Ding, Changying and Peterson, Jesse},
  title         = {Biexact von {N}eumann algebras},
  year          = {2023},
  eprint        = {2309.10161},
  archivePrefix = {arXiv},
}
@misc{peterson-f4,
  author       = {Peterson, Jesse},
  title        = {Open problems in operator algebras},
  howpublished = {Web page},
  year         = {2026},
  url          = {https://www.math.uwaterloo.ca/~j37peter/problems.html},
  note         = {Problem F.4; version of 15 May 2026},
}
@article{ding2023proximal,
  author  = {Ding, Changying and Kunnawalkam Elayavalli, Srivatsav and Peterson, Jesse},
  title   = {Properly proximal von {N}eumann algebras},
  journal = {Duke Math. J.},
  volume  = {172},
  number  = {15},
  pages   = {2821--2894},
  year    = {2023},
  doi     = {10.1215/00127094-2022-0098},
}

Citing this problem

This identifier is permanent. It will not change if the problem is solved, reclassified or withdrawn.

OP-01002, "Biexactness of the bidual of the reduced C*-algebra of F₂", clopen.solutions.