Haagerup property of semigroup crossed products

被引：1
|
作者：
Meng, Qing [1 ]
机构：
[1] Qufu Normal Univ, Sch Math Sci, Qufu 273165, Shandong, Peoples R China
来源：
QUAESTIONES MATHEMATICAE | 2023年 / 46卷 / 11期
基金：
中国国家自然科学基金;
关键词：
Primary; Haagerup property; semigroup crossed product; lattice ordered group; APPROXIMATION PROPERTY;
D O I：
10.2989/16073606.2022.2146019
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study the Haagerup property of semigroup crossed products for lattice ordered groups. Let G be a lattice ordered group. We show that the reduced semigroup C*-algebra C*(r) (G+) has the Haagerup property if and only if G has the Haagerup property. Let G act on a unital C*-algebra A through an action a, we show that if the reduced semigroup crossed product A xl(a,r) G+ has the Haagerup property, then both A and G have the Haagerup property. On the other hand, it is shown that if G is s-amenable and A has the Haagerup property, then A xl(a,r) G+ has the Haagerup property.
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页码：2437 / 2451
页数：15
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