QWEP stability under twisted crossed products

@misc{zeng2026qwep,
  title = {{QWEP stability under twisted crossed products}},
  author = {Kai ZENG},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.03424},
  eprint = {2610.03424},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.03424},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - QWEP stability under twisted crossed products
AU  - Kai ZENG
PY  - 2026
DA  - 2026/10/02
PB  - arXiv
DO  - 10.48550/arxiv.2610.03424
UR  - https://arxiv.org/abs/2610.03424
AB  - We study the QWEP property of twisted crossed products and its relation to Fourier multiplier transference on noncommutative L_p-spaces. We show that QWEP is not preserved by crossed products of QWEP von Neumann algebras by hyperlinear groups. Our examples include trace-preserving actions of a torsion-free residually finite Kazhdan group on a diffuse abelian algebra and on the hyperfinite type II_1 factor. We also obtain non-QWEP crossed products with nontrivial scalar cocycles. For scalar twists, we prove that a finite trace-preserving crossed product is QWEP if and only if its ordinary crossed product and its twisted group von Neumann algebra are QWEP. In the positive direction, we establish a restriction theorem for scalar twists of regular wreath products. These results provide QWEP inputs for Fourier multiplier transference and identify a completely bounded multiplier norm obstruction to QWEP. Finally, operator-valued cocycles give finite QWEP crossed products whose acting groups are not hyperlinear.
ER  -