Property T and Amenable Transformation Group $C^*$-algebras

Canadian mathematical bulletin

F. Kamalov¹ 

[1] Mathematics Department, Canadian University of Dubai, Dubai, UAE

关键词: Property T;    $C^*$-algebras;    transformation group;    amenable;   

DOI  :  10.4153/CMB-2014-006-5

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

It is well known that a discrete group which is both amenable andhas Kazhdan's Property T must be finite. In this note we generalizethe above statement to the case of transformation groups. We showthat if $G$ is a discrete amenable group acting on a compactHausdorff space $X$, then the transformation group $C^*$-algebra$C^*(X, G)$ has Property T if and only if both $X$ and $G$ are finite. Ourapproach does not rely on the use of tracial states on $C^*(X, G)$.

【 授权许可】

Unknown