{"title":"The roots of elements of Aut(SH2)","authors":"A. Mirzapour, R. Eskandari","doi":"10.7153/oam-2023-17-12","DOIUrl":null,"url":null,"abstract":". We study the roots of automorphisms on the Siegel upper half plane of complex di-mension three. We use the normal form of any element of Sp ( 2 , R ) under the conjugation in Sp ( 2 , R ) to show that some of automorphisms have roots and that some of them do not have. As an application, we generalize the Siegel unit disk of the same dimension.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.7153/oam-2023-17-12","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
. We study the roots of automorphisms on the Siegel upper half plane of complex di-mension three. We use the normal form of any element of Sp ( 2 , R ) under the conjugation in Sp ( 2 , R ) to show that some of automorphisms have roots and that some of them do not have. As an application, we generalize the Siegel unit disk of the same dimension.
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