On Quantum Duality of Group Amenability

Symmetry

Xia Zhang¹  Ming Liu¹ 

[1] School of Mathematical Sciences, Tiangong University, Tianjin 300387, China;

关键词: compact quantum group;    quantum duality;    amenability;    co-amenability;    quantum double construction;    haar integral;   

DOI  :  10.3390/sym12010085

来源: DOAJ

【 摘 要 】

In this paper, we investigate the co-amenability of compact quantum groups. Combining with some properties of regular C*-norms on algebraic compact quantum groups, we show that the quantum double of co-amenable compact quantum groups is unique. Based on this, this paper proves that co-amenability is preserved under formulation of the quantum double construction of compact quantum groups, which exhibits a type of nice symmetry between the co-amenability of quantum groups and the amenability of groups.

【 授权许可】

Unknown