论文标题
关于行动的二元性
On dualities of actions
论文作者
论文摘要
我们介绍了离散组动作在unital $ c^*$ - 代数上的弱纹身近似表示的概念，该代数可能没有像江-su代数$ \ mathcal {z} $这样的预测。然后，我们在弱的曲折rokhlin特性与弱曲折的近似能力之间表现出双重性。更确切地说，当$ g $是有限的阿贝尔集团，而$α：g \ curvearrowright a $是对Unital简单的无限尺寸$ C^*$ - 代数的组动作，我们证明这一点 当$ \hatα$具有较弱的曲折近似能力时，1。$α$具有较弱的曲折rokhlin属性。 2。$α$具有较弱的曲折近似能力，并且仅当$ \hatα$具有较弱的曲折rokhlin属性时。
We introduce the notion of the weak tracial approximate representability of a discrete group action on a unital $C^*$-algebra which could have no projections like the Jiang-Su algebra $\mathcal{Z}$. Then we show a duality between the weak tracial Rokhlin property and the weak tracial approximate representability. More precisely, when $G$ is a finite abelian group and $α:G\curvearrowright A$ is a group action on a unital simple infinite dimensional $C^*$-algebra, we prove that 1. $α$ has the weak tracial Rokhlin property if and only if $\hatα$ has the weak tracial approximate representability. 2. $α$ has the weak tracial approximate representability if and only if $\hatα$ has the weak tracial Rokhlin property.
