Report
QWEP stability under twisted crossed products
| Title: | QWEP stability under twisted crossed products |
|---|---|
| Authors: | ZENG, Kai |
| Publication Year: | 2026 |
| Subject Terms: | Operator Algebras, Functional Analysis, Group Theory |
| Description: | 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. First version, 20 pages |
| Document Type: | Working Paper |
| DOI: | 10.48550/arXiv.2610.03424 |
| Access URL: | https://arxiv.org/abs/2610.03424 |
| Accession Number: | edsarx.2610.03424 |
| Database: | arXiv |
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