论文标题
非主要扭曲的groupoid $ c^*$ - 代数的cartan子代理
Cartan subalgebras for non-principal twisted groupoid $C^*$-algebras
论文作者
论文摘要
雷诺（Renault）在2008年证明，如果$ g $是拓扑主体群体，那么$ c_0（g^{（0）}）$是$ c^*_ r（g，σ）$的cartan subalgebra，对于$ g $而言，$ c $σ$。但是，有许多群体不是拓扑主体的，但它们（扭曲的）$ c^*$ - 代数允许cartan subgerbras。本文通过识别$ g $上的2循环$ c $的条件和$ c^*_ r（s，c）$是$ c^*_ r（g，c）$的cartan cartan，对这类cartan subselgebras进行了动态描述。当$ g $是一个离散的组时，我们还描述了与这些cartan对相关的weyl groupoid和twist，在轻度的其他假设下。
Renault proved in 2008 that if $G$ is a topologically principal groupoid, then $C_0(G^{(0)})$ is a Cartan subalgebra in $C^*_r(G, Σ)$ for any twist $Σ$ over $G$. However, there are many groupoids which are not topologically principal, yet their (twisted) $C^*$-algebras admit Cartan subalgebras. This paper gives a dynamical description of a class of such Cartan subalgebras, by identifying conditions on a 2-cocycle $c$ on $G$ and a subgroupoid $S \subseteq G$ under which $C^*_r(S, c)$ is Cartan in $C^*_r(G, c)$. When $G$ is a discrete group, we also describe the Weyl groupoid and twist associated to these Cartan pairs, under mild additional hypotheses.
