Do the group factors of PSLₙ(ℤ) remember n?

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Source: S. Popa, Some open problems in W*-rigidity (2013), as a case of Connes's rigidity conjecture; listed as R.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

Secondary

GR

Keywords

group von Neumann algebras, lattices in Lie groups, Peterson's operator algebra problems, W*-rigidity

References

@misc{popa2013problems-r4,
  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-r4,
  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.4; version of 15 May 2026},
}
@article{cowling1989-r4,
  author  = {Cowling, Michael and Haagerup, Uffe},
  title   = {Completely bounded multipliers of the {F}ourier algebra of a simple {L}ie group of real rank one},
  journal = {Invent. Math.},
  volume  = {96},
  number  = {3},
  pages   = {507--549},
  year    = {1989},
  doi     = {10.1007/BF01393695},
}
@article{connesjones1985,
  author  = {Connes, Alain and Jones, Vaughan},
  title   = {Property {T} for von {N}eumann algebras},
  journal = {Bull. Lond. Math. Soc.},
  volume  = {17},
  number  = {1},
  pages   = {57--62},
  year    = {1985},
  doi     = {10.1112/blms/17.1.57},
}

Resolution claims

Status history

Citing this problem

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OP-01058, "Do the group factors of PSLₙ(ℤ) remember n?", clopen.solutions.