A full description of property T of unital C*-crossed products

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:483

Article

Meng, Qing¹  Ng, Chi-Keung^2,3 

[1] Qufu Normal Univ, Sch Math Sci, Qufu 273165, Shandong, Peoples R China

[2] Nankai Univ, Chern Inst Math, Tianjin 300071, Peoples R China

[3] Nankai Univ, LPMC, Tianjin 300071, Peoples R China

关键词: C*-crossed products;    Property T;    Strong property T;   

DOI  :  10.1016/j.jmaa.2019.123637

来源: Elsevier

【 摘 要 】

Let Gamma be a discrete group that acts on a unital C*-algebra A through an action beta. We study property T as well as its stronger variant of the full and the reduced crossed products. We show that if A has a beta-invariant tracial state, then the reduced crossed product A (sic) (beta,r) Gamma has strong property T if and only if Gamma has property T and (A (sic) (beta,r )Gamma, A) has strong property T. If Gamma has the Haagerup property, the strong property T of (A (sic) (beta,r) Gamma, A) in the above statement can be replaced by that of A. Furthermore, the strong property T of the full crossed product is shown to coincide with that of the reduced one. In the case of property T, we obtain the corresponding result when the group is either ICC or abelian. As an application, a non-compact locally compact group G is amenable if and only if C-b(G) (sic)(It ,r) G(d) does not have strong property T, where G(d) is the group G equipped with the discrete topology and It is the left translation action. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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