OP-00974 Open

Nonamenable subfactors of the free group factor L(F₂)

Here a subfactor of $L(\mathbb F_2)$ is a von Neumann subalgebra that is a factor, and the interpolated free group factors are the factors $L(\mathbb F_t)$, $1 < t \le \infty$, of Dykema and Rădulescu.

Problem. Is every nonamenable subfactor of $L(\mathbb F_2)$ isomorphic to an interpolated free group factor?

Source: Listed without attribution in S. Popa, Some open problems in W*-rigidity (2013), and as F.1 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: free group factors, interpolated free group factors, Peterson's operator algebra problems, subfactors
Literature checked: Oct. 26, 2026 by clemens-admin

References

@misc{popa2013problems-f1,
  author       = {Popa, Sorin},
  title        = {Some open problems in {W}$^*$-rigidity},
  howpublished = {Slides, Paris, June 2013},
  year         = {2013},
  url          = {https://www.math.ucla.edu/~popa/ProblemsJune2013.pdf},
}
@misc{peterson-f1,
  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.1; version of 15 May 2026},
}
@article{hayes2025,
  author  = {Hayes, Ben and Jekel, David and Kunnawalkam Elayavalli, Srivatsav},
  title   = {Consequences of the random matrix solution to the {P}eterson--{T}hom conjecture},
  journal = {Anal. PDE},
  volume  = {18},
  number  = {7},
  pages   = {1805--1834},
  year    = {2025},
  doi     = {10.2140/apde.2025.18.1805},
}
@article{houdayer2010,
  author  = {Houdayer, Cyril},
  title   = {Strongly solid group factors which are not interpolated free group factors},
  journal = {Math. Ann.},
  volume  = {346},
  number  = {4},
  pages   = {969--989},
  year    = {2010},
  doi     = {10.1007/s00208-009-0417-6},
}
@article{ozawapopa2010,
  author  = {Ozawa, Narutaka and Popa, Sorin},
  title   = {On a class of {II}$_1$ factors with at most one {C}artan subalgebra},
  journal = {Ann. of Math.},
  volume  = {172},
  number  = {1},
  pages   = {713--749},
  year    = {2010},
  doi     = {10.4007/annals.2010.172.713},
}
@article{ozawa2004,
  author  = {Ozawa, Narutaka},
  title   = {Solid von {N}eumann algebras},
  journal = {Acta Math.},
  volume  = {192},
  number  = {1},
  pages   = {111--117},
  year    = {2004},
  doi     = {10.1007/BF02441087},
}

Citing this problem

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 It will not change if the problem is solved, reclassified or withdrawn.

OP-00974, "Nonamenable subfactors of the free group factor L(F₂)", clopen.solutions.