Property T and amenable transformation group C∗-algebras

Date

2014

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

DOI