论文标题
Kirillov理论$ C^*（g，ω）$
Kirillov theory for $C^*(G,Ω)$
论文作者
论文摘要
让$ g $成为一个简单连接的nilpotent Lie Group，lie代数$ \ frak g $;令$ \ frak g^*$为$ \ frak g $的双重。让$ω$成为具有连续$ g $ Action的本地紧凑型豪斯多夫空间，然后让$ c^*（g，ω）$为相应的转换组$ c^*$ algebra。我们从商空间中构造一个连续的滤波映射$ ϕ $，$ \ frak g^*\ timesome/\ sim $，这是$ \ frak g^*\ timesmomomomomomomomomomomomomomomomomomation $（c^*（g，g，ω））$的同型同态。 我们还描述了$ c^*（g，ω）$的角色理论，该理论概括了$ g $的Kirillov角色理论。
Let $G$ be a simply connected nilpotent Lie group with Lie algebra $\frak g$; let $\frak g^*$ be the dual of $\frak g$. Let $Ω$ be a locally compact second countable Hausdorff space with a continuous $G$ action, and let $C^*(G,Ω)$ be the corresponding transformation group $C^*$ algebra. We construct a continuous surjective map $ϕ$ from a quotient space, $\frak g^*\timesΩ/\sim$, which is a homeomorphism from $\frak g^*\timesΩ/\sim$ to Prim$(C^*(G,Ω))$. We also describe a character theory for $C^*(G,Ω)$ which generalizes Kirillov character theory for $G$.
