Geodesic
Property T and Amenable Transformation Group C*-algebras
Canadian mathematical bulletin, Tome 58 (2015) no. 1, pp. 110-114

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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 ${{C}^{*}}\left( X,\,G \right)$ .
DOI : 10.4153/CMB-2014-006-5
Mots-clés : 46L55, 46L05, Property T, C*-algebras, transformation group, amenable 
Kamalov, F. Property T and Amenable Transformation Group C*-algebras. Canadian mathematical bulletin, Tome 58 (2015) no. 1, pp. 110-114. doi: 10.4153/CMB-2014-006-5
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