QWEP stability under twisted crossed products

Kai ZENG

Home/Archive/arXiv

arXiv · 2610.03424

QWEP stability under twisted crossed products

Kai ZENG

View original source ↗Read source document ↗Export metadata ↓

Abstract

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.

Explore related subjects

math.OA math.FA math.GR

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Kai ZENG. 2026-10-02. QWEP stability under twisted crossed products. https://arxiv.org/abs/2610.03424

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Quantum Graph Theory by Example

Quantum graphs have been introduced by Duan, Severini, and Winter to describe the zero-error behaviour of quantum channels. Since then, quantum graph theory has become a field of study in its own right. A substantial source of difficulty in working with quantum graphs compared to classical graphs stems from the fact that they are no longer discrete objects. This makes it generally difficult to construct insightful, non-trivial examples. We present a collection of non-trivial quantum graphs that can be thought of in discrete terms, and that can be expressed in the diagrammatic formalism introduced by Musto, Reutter, and Verdon. The examples arise as the quantum graphs acted on by increasingly smaller classical matrix groups, and are parametrised by triples of matrices $(A, B, C)$. The parametrisation reveals a clean decomposition of quantum graph structure into classical and genuinely quantum components: $A$ and $C$ are described by a classical weighted graph called the strange graph, while $B$ provides a purely quantum contribution with no classical analogue. Based on this model, we give exact formulas or establish bounds for quantum graph parameters, such as the number of connected components, the chromatic number, the independence number, and the clique number. Our results provide the first large, parametric families of quantum graphs for which standard graph parameters can be computed analytically.

math.OA↗

arXiv2026

Weak type $(1,1)$ boundedness of Bochner--Riesz means at the critical index on quantum tori

We establish a weak type $(1,1)$ estimate for the Bochner--Riesz mean operator at the critical index $δ=\frac{d-1}{2}$ on the quantum torus $\mathbb{T}^d_θ$, where the associated kernel is rough.

math.OA↗

arXiv2026

Talagrand type for noncommutative $L_1$ spaces

Let $(\mathcal{M},τ)$ be a semi-finite von Neumann algebra. We prove that $L_1(\mathcal{M})$ has Talagrand type $(1,ψ_{1,1})$, where $ψ_{1,1}(t)=t/\log(e+t)$. As an consequence, the Schatten trace class $S_1$ has Talagrand type $(1,ψ_{1,1})$, thus settled an open problem of Question 2 in Cordero-Erausquin and Eskenazis (2023). Our proof is based on the noncommutative Mazur maps initiated by Ricard.

math.OA↗