论文标题
（非）各向同性基团组代数的异国情调完成
(Non)exotic completions of the group algebras of isotropy groups
论文作者
论文摘要
在降低的C $^*$ - étaleGroupoids代数上表征KMS状态的问题的动机，我们表明，这些代数的降低的规范会导致同型组的组代数的C $^*$ - 规范。这种c $^*$ - 规范与变换群体的规范减少相吻合，但是，如Higson-Lafforgue-Skandalis的示例所示，对于与小组动作相关的细菌的群体素质可能已经是异国情调的。我们表明，对于某些类别的分组类固醇，对于与组的部分作用相关的群体素，以及与组的半方向产物相关的群体和类别均具有正态的各向同性基团的半程产物的群体素，尤其是标准的规范。
Motivated by the problem of characterizing KMS states on the reduced C$^*$-algebras of étale groupoids, we show that the reduced norm on these algebras induces a C$^*$-norm on the group algebras of the isotropy groups. This C$^*$-norm coincides with the reduced norm for the transformation groupoids, but, as follows from examples of Higson-Lafforgue-Skandalis, it can be exotic already for groupoids of germs associated with group actions. We show that the norm is still the reduced one for some classes of graded groupoids, in particular, for the groupoids associated with partial actions of groups and the semidirect products of exact groups and groupoids with amenable isotropy groups.
