Property T and amenable transformation group C∗-algebras

Date
2014
Authors
Kamalov, Firuz
Journal Title
Journal ISSN
Volume Title
Publisher
Canadian Mathematical Society
Abstract
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.
Description
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: https://doi.org/10.4153/CMB-2014-006-5.
Keywords
Amenable, C∗-algebras, Property T, Transformation group
Citation
Kamalov, F. (2014). Property T and amenable transformation group C∗-algebras. Canadian Mathematical Bulletin, 58(1), 110–114. https://doi.org/10.4153/CMB-2014-006-5