论文标题
动态的Kirchberg-Phillips定理
The dynamical Kirchberg-Phillips theorem
论文作者
论文摘要
令$ g $为第二个可当地的紧凑型组。在本文中，我们研究了Kirchberg代数上的$ G $ actions，该代数承认对Cuntz代数$ \ MATHCAL {O} _ \ infty $的无规范准行动的中心嵌入。如果$ g $是离散的，那么这与Kirchberg代数上的Amenable和外部$ G $ ACTIONS相吻合。我们表明，由此产生的$ g $ -c*动力学系统由等效的卡斯帕罗夫理论分类为共轭。这是适用于任意局部紧凑型组的行动的第一个分类理论。在各种应用中，我们的主要结果解决了iZumi的猜想，用于离散的无扭转组的动作，并恢复了izumi-Matui最近工作的主要结果，用于poly- $ $ $ $ \ mathbb {Z} $组的作用。
Let $G$ be a second-countable, locally compact group. In this article we study amenable $G$-actions on Kirchberg algebras that admit an approximately central embedding of a canonical quasi-free action on the Cuntz algebra $\mathcal{O}_\infty$. If $G$ is discrete, this coincides with the class of amenable and outer $G$-actions on Kirchberg algebras. We show that the resulting $G$-C*-dynamical systems are classified by equivariant Kasparov theory up to cocycle conjugacy. This is the first classification theory of its kind applicable to actions of arbitrary locally compact groups. Among various applications, our main result solves a conjecture of Izumi for actions of discrete amenable torsion-free groups, and recovers the main results of recent work by Izumi-Matui for actions of poly-$\mathbb{Z}$ groups.
