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

  • F. Kamalov,
    Mathematics Department, Canadian University of Dubai, Dubai, UAE
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Abstract

It is well known that a discrete group which is both amenable and has Kazhdan's Property T must be finite. In this note we generalize the above statement to the case of transformation groups. We show that if $G$ is a discrete amenable group acting on a compact Hausdorff space $X$, then the transformation group $C^*$-algebra $C^*(X, G)$ has Property T if and only if both $X$ and $G$ are finite. Our approach does not rely on the use of tracial states on $C^*(X, G)$.
Keywords: Property T, $C^*$-algebras, transformation group, amenable Property T, $C^*$-algebras, transformation group, amenable
MSC Classifications: 46L55, 46L05 show english descriptions Noncommutative dynamical systems [See also 28Dxx, 37Kxx, 37Lxx, 54H20]
General theory of $C^*$-algebras
46L55 - Noncommutative dynamical systems [See also 28Dxx, 37Kxx, 37Lxx, 54H20]
46L05 - General theory of $C^*$-algebras
 

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