Outer automorphisms of group factors of hyperbolic property (T) groups

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Source: J. Peterson, AimPL problem list Classification of group von Neumann algebras (2018), Problem 2.3, where a remark adds the hyperbolicity assumption; listed as R.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

Secondary

GR

Keywords

hyperbolic groups, outer automorphism groups, Peterson's operator algebra problems, property (T), W*-rigidity

Literature checked

Oct. 26, 2026 by clemens-admin

References

@misc{aimpl2018-r7,
  title        = {{AimPL}: Classification of group von {N}eumann algebras},
  howpublished = {AIM problem list},
  year         = {2018},
  url          = {http://aimpl.org/groupvonneumann},
  note         = {Problem 2.3},
}
@misc{peterson-r7,
  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 R.7; version of 15 May 2026},
}
@incollection{paulin1991,
  author    = {Paulin, Fr{\'e}d{\'e}ric},
  title     = {Outer automorphisms of hyperbolic groups and small actions on {$\mathbb R$}-trees},
  booktitle = {Arboreal group theory (Berkeley, CA, 1988)},
  series    = {Math. Sci. Res. Inst. Publ.},
  volume    = {19},
  publisher = {Springer},
  pages     = {331--343},
  year      = {1991},
  doi       = {10.1007/978-1-4612-3142-4_12},
}
@article{chifan2026out,
  author  = {Chifan, Ionu{\c t} and Ioana, Adrian and Osin, Denis and Sun, Bin},
  title   = {Wreath-like products of groups and their von {N}eumann algebras {II}: outer automorphisms},
  journal = {Duke Math. J.},
  volume  = {175},
  number  = {2},
  pages   = {287--359},
  year    = {2026},
  doi     = {10.1215/00127094-2025-0028},
}
@misc{openai2026lattice,
  author       = {{OpenAI}},
  title        = {The arithmetic category and stable recovery of lattice factors},
  howpublished = {github.com/openai/math, family 286},
  year         = {2026},
  url          = {https://github.com/openai/math/tree/1581d4cbdd69a0faf34b2089614fe2a814316a6a/preprints/The-arithmetic-category-and-stable-recovery-of-lattice-factors-September-23-2026},
  note         = {Model-written manuscript, 23 Sep 2026, not refereed; Corollary (Outer automorphisms) claims Out(L Gamma) = Hom(Gamma,T) x| Out(Gamma) for its class of lattices, which include icc cocompact lattices in Sp(n,1), n >= 2, and F_4(-20)},
}

Citing this problem

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 It will not change if the problem is solved, reclassified or withdrawn.

OP-00994, "Outer automorphisms of group factors of hyperbolic property (T) groups", clopen.solutions.