Evans-Kishimoto type argument for actions of discrete amenable groups on McDuff factors

Classification of minimal actions of a compact Kac algebra with amenable dual

We show the uniqueness of minimal actions of a compact Kac algebra with amenable dual on the AFD factor of type II$_1$. This particularly implies the uniqueness of minimal actions of a compact group. Our main tools are a Rohlin type theorem, the 2-cohomology vanishing theorem, and the Evans-Kishimoto type intertwining argument.

离散顺从群到遍历变换全群正规化子的作用

Actions of discrete amenable groups into the normalizers of full groups of ergodic transformations

本文利用Evans-Kishimoto交织论证对离散顺从群到遍历变换全群正规化子的作用进行分类，且证明不依赖遍历变换的类型。

Crossed products by finite cyclic group actions with the tracial Rokhlin property

We define the tracial Rokhlin property for actions of finite cyclic groups on stably finite simple unital C*-algebras. We prove that when the algebra is in addition simple and has tracial rank zero, then the crossed product again has tracial rank zero. Under a kind of weak approximate innerness assumption and one other technical condition, we prove that if the action has the the tracial Rokhlin property and the crossed product has tracial rank zero, then the original algebra has tracial rank zero. We give examples showing how the tracial Rokhlin property differs from the Rokhlin property of Iz…