论文标题
groupoid Actions和Koopman表示
Groupoid actions and Koopman representations
论文作者
论文摘要
我们研究$ c^*$ - 代数$ c^*（κ）$由koopman表示产生的$κ=κ=κ^μ$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ g $作用于量度空间$（x，μ）$，其中$μ$是quasi ins quasi-Insi-Invariant用于该动作。我们将$κ$解释为一种引起的表示形式，我们证明，如果Groupoid $ g \ ltimes x $是可修正的，那么$κ$在常规表示中薄弱地包含$ρ=ρ^μ$，因此我们有透明的同构$ c^*_ r（g）\ r（g）\ to c^*c^*（κ）$。我们考虑雷诺 - deaconu groupoids $ g = g = g（x，t）$的特殊情况，该$在其单位空间$ x $上作用，并表明在某些情况下，$ c^*（κ）\ cong c^*（g）$。
We study the $C^*$-algebra $C^*(κ)$ generated by the Koopman representation $κ=κ^μ$ of a locally compact groupoid $G$ acting on a measure space $(X,μ)$, where $μ$ is quasi-invariant for the action. We interpret $κ$ as an induced representation and we prove that if the groupoid $G\ltimes X$ is amenable, then $κ$ is weakly contained in the regular representation $ρ=ρ^μ$ associated to $μ$, so we have a surjective homomorphism $C^*_r(G)\to C^*(κ)$. We consider the particular case of Renault-Deaconu groupoids $G= G(X,T)$ acting on their unit space $X$ and show that in some cases $C^*(κ)\cong C^*(G)$.
