{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:11:11Z","timestamp":1760145071896,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2024,6,12]],"date-time":"2024-06-12T00:00:00Z","timestamp":1718150400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation of Jiangsu Province","award":["BK20210783"],"award-info":[{"award-number":["BK20210783"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Let D(Rm,n(q)) be the Drinfeld double of Radford Hopf algebra Rm,n(q) and D(Hs,t) be the Drinfeld double of generalized Taft algebra Hs,t. Both D(Rm,n(q)) and D(Hs,t) have very symmetric structures. We calculate all Hopf automorphisms of D(Rm,n(q)) and D(Hs,t), respectively. Furthermore, we prove that the Hopf automorphism group AutHopf(D(Rm,n(q))) is isomorphic to the direct sum Zn\u2a01Zm of cyclic groups Zm and Zn, the Hopf automorphism group AutHopf(D(Hs,t)) is isomorphic to the semi-direct products k*\u22caZd of multiplicative group k* and cyclic group Zd, where s=td,k*=k\\{0}, and k is an algebraically closed field with char (k)\u2224t.<\/jats:p>","DOI":"10.3390\/sym16060735","type":"journal-article","created":{"date-parts":[[2024,6,14]],"date-time":"2024-06-14T08:52:10Z","timestamp":1718355130000},"page":"735","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Hopf Automorphism Group of Two Classes of Drinfeld Doubles"],"prefix":"10.3390","volume":"16","author":[{"given":"Hua","family":"Sun","sequence":"first","affiliation":[{"name":"College of Mathematical Science, Yangzhou University, Yangzhou 225002, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mi","family":"Hu","sequence":"additional","affiliation":[{"name":"College of Mathematical Science, Yangzhou University, Yangzhou 225002, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiawei","family":"Hu","sequence":"additional","affiliation":[{"name":"College of Mathematical Science, Yangzhou University, Yangzhou 225002, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,6,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"757","DOI":"10.1007\/s10468-018-9797-1","article-title":"Stable Green Ring of the Drinfeld Doubles of the Generalised Taft Algebras (Corrections and New Results)","volume":"22","author":"Erdmann","year":"2019","journal-title":"Algebr. 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