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Open AccessArticle

On Quantum Duality of Group Amenability

by Xia Zhang and Ming Liu *,†
School of Mathematical Sciences, Tiangong University, Tianjin 300387, China
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Symmetry 2020, 12(1), 85; https://doi.org/10.3390/sym12010085
Received: 3 November 2019 / Revised: 24 December 2019 / Accepted: 27 December 2019 / Published: 2 January 2020
(This article belongs to the Special Issue Advance in Nonlinear Analysis and Optimization)
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. View Full-Text
Keywords: compact quantum group; quantum duality; amenability; co-amenability; quantum double construction; Haar integral compact quantum group; quantum duality; amenability; co-amenability; quantum double construction; Haar integral
MDPI and ACS Style

Zhang, X.; Liu, M. On Quantum Duality of Group Amenability. Symmetry 2020, 12, 85.

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