发表机构
KU Leuven; Leipzig University（荷语鲁汶大学; 莱比锡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过模导子提出冯·诺依曼代数的相对粗刚性概念，扩展L²-刚性至非迹情形，并证明无相对amenable项时形变收敛，从而统一证明完全性等不可分解性质。
AI 中文摘要
我们通过模导子及其相关的GNS-对称量子马尔可夫半群，为σ-有限的冯·诺依曼代数提出了一种相对粗刚性的概念，将Peterson的L²-刚性框架扩展到非迹情形。我们的主要结果表明，不存在相对 amenable 的直和项会迫使相关的形变在超幂中的相对交换子上收敛。对于具有可分预对偶的扩散冯·诺依曼代数，这产生了在存在 amenable 直和项与关于中心序列的刚性之间的二分法。这些结果为证明不可分解性质（如完全性、相对ω-固态性和相对稳定固态性）提供了一种新颖的统一方法。我们的方法适用于诸如融合自由积、算子值自由Araki-Woods因子和余循环交叉积等例子。
英文摘要
We propose a notion of relative coarse rigidity for $σ$-finite von Neumann algebras through modular derivations and their associated GNS-symmetric quantum Markov semigroups, extending Peterson's framework of $L^2$-rigidity to the nontracial setting. Our main result shows that the absence of relatively amenable summands forces the associated deformations to converge on relative commutants in ultrapowers. For diffuse von Neumann algebras with separable predual, this yields a dichotomy between the presence of an amenable summand and rigidity in terms of central sequences. These results give a novel unified approach for proving indecomposability properties such as fullness, relative $ω$-solidity and relative stable solidity. Our methods apply to examples such as amalgamated free products, operator-valued free Araki-Woods factors and cocycle crossed products.
Comments75 pages
