Property T and amenable transformation group C∗-algebras

Kamalov, Firuz
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Canadian Mathematical Society
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∗(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). Copyright © 2014 Canadian Mathematical Society.
This article is not available at CUD collection. The version of scholarly record of this Article is published in Canadian Mathematical Bulletin (2014), available online at:
Amenable, C∗-algebras, Property T, Transformation group
Kamalov, F. (2014). Property T and amenable transformation group C∗-algebras. Canadian Mathematical Bulletin, 58(1), 110–114.