OP-00965 Open

Tensor factors of McDuff II₁ factors

Problem. Let $M_1$ and $M_2$ be II$_1$ factors such that $M_1 \mathbin{\overline\otimes} M_2$ is McDuff. Must $M_1$ or $M_2$ be McDuff?

Source: Stated as Conjecture D by A. Marrakchi (2018); listed as S.7 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: central sequences, McDuff factors, Peterson's operator algebra problems, tensor products
Literature checked: Oct. 26, 2026 by clemens-admin

References

@article{marrakchi2018,
  author  = {Marrakchi, Amine},
  title   = {Stability of products of equivalence relations},
  journal = {Compos. Math.},
  volume  = {154},
  number  = {9},
  pages   = {2005--2019},
  year    = {2018},
  doi     = {10.1112/S0010437X18007388},
}
@misc{peterson-s7,
  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 S.7; version of 15 May 2026},
}
@article{hashiba2022,
  author  = {Hashiba, Yasuhito},
  title   = {On central sequence algebras of tensor product von {N}eumann algebras},
  journal = {Publ. Res. Inst. Math. Sci.},
  volume  = {58},
  number  = {2},
  pages   = {441--449},
  year    = {2022},
  doi     = {10.4171/PRIMS/58-2-6},
}
@article{mcduff1970,
  author  = {McDuff, Dusa},
  title   = {Central sequences and the hyperfinite factor},
  journal = {Proc. Lond. Math. Soc.},
  volume  = {s3-21},
  number  = {3},
  pages   = {443--461},
  year    = {1970},
  doi     = {10.1112/plms/s3-21.3.443},
}

Citing this problem

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 It will not change if the problem is solved, reclassified or withdrawn.

OP-00965, "Tensor factors of McDuff II₁ factors", clopen.solutions.