{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T00:41:23Z","timestamp":1760402483866,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,1,2]],"date-time":"2020-01-02T00:00:00Z","timestamp":1577923200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11301380"],"award-info":[{"award-number":["11301380"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the National Natural Science Foundation of Tianjin","award":["18JCYBJC18900"],"award-info":[{"award-number":["18JCYBJC18900"]}]},{"name":"the Higher School Science and Technology Development Fund Project in Tianjin","award":["20131003"],"award-info":[{"award-number":["20131003"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/sym12010085","type":"journal-article","created":{"date-parts":[[2020,1,3]],"date-time":"2020-01-03T11:55:07Z","timestamp":1578052507000},"page":"85","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On Quantum Duality of Group Amenability"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7955-0341","authenticated-orcid":false,"given":"Xia","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Tiangong University, Tianjin 300387, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4899-0333","authenticated-orcid":false,"given":"Ming","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Tiangong University, Tianjin 300387, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,1,2]]},"reference":[{"key":"ref_1","unstructured":"Woronowicz, S.L. 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