location:  Publications → journals → CMB
Abstract view

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

Published:2014-02-25
Printed: Mar 2015
• F. Kamalov,
Mathematics Department, Canadian University of Dubai, Dubai, UAE
 Format: LaTeX MathJax PDF

## 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
 MSC Classifications: 46L55 - Noncommutative dynamical systems [See also 28Dxx, 37Kxx, 37Lxx, 54H20] 46L05 - General theory of $C^*$-algebras

 top of page | contact us | privacy | site map |