发表机构
Ghent University（根特大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究扭曲交叉积的QWEP性质，证明其不被超线性群交叉积保持，给出非QWEP例子，并建立标量扭曲下QWEP的等价条件及正则圈积的限制定理，为Fourier乘子转移提供输入并识别范数障碍。
AI 中文摘要
我们研究了扭曲交叉积的QWEP性质及其与非交换$L_p$空间上Fourier乘子转移的关系。我们证明，对于超线性群的交叉积，QWEP性质不被保持：即QWEP von Neumann代数与超线性群的交叉积不一定具有QWEP。我们的例子包括一个无挠的剩余有限Kazhdan群在扩散交换代数及超有限II$_1$因子上的保迹作用。我们还构造了具有非平凡标量余循环的非QWEP交叉积。对于标量扭曲，我们证明：一个有限保迹交叉积具有QWEP当且仅当其普通交叉积及其扭曲群von Neumann代数均具有QWEP。在正面方向上，我们建立了正则圈积的标量扭曲的限制定理。这些结果为Fourier乘子转移提供了QWEP输入，并识别出一个完全有界乘子范数障碍，阻碍QWEP性质。最后，算子值余循环给出了有限QWEP交叉积，但其作用群不是超线性的。
英文摘要
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.
CommentsFirst version, 20 pages
