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Property T and Amenable Transformation Group C*-algebras

Published online by Cambridge University Press:  20 November 2018

F. Kamalov
F. Kamalov*
Affiliation:
Mathematics Department, Canadian University of Dubai, Dubai, UAE. e-mail: firuz@cud.ac.ae
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Abstract

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It is well known that a discrete group that is both amenable and has Kazhdan’s Property $T$ must be finite. In this note we generalize this 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 ${{C}^{*}}\left( X,\,G \right)$ 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 ${{C}^{*}}\left( X,\,G \right)$.

Keywords

46L5546L05Property TC*-algebrastransformation groupamenable
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 58 , Issue 1 , 01 March 2015 , pp. 110 - 114
Copyright
Copyright © Canadian Mathematical Society 2015

References

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