{"title":"无常环的自变形和扭曲形式","authors":"János Kollár","doi":"10.1007/s00032-024-00403-x","DOIUrl":null,"url":null,"abstract":"<p>Let <span>\\(G\\subset \\textrm{GL}_n(k)\\)</span> be a finite subgroup and <span>\\(k[x_1,\\dots , x_n]^G\\subset k[x_1,\\dots , x_n]\\)</span> its ring of invariants. We show that, in many cases, the automorphism group of <span>\\(k[x_1,\\dots , x_n]^G\\)</span> is <span>\\(k^\\times \\)</span>.</p>","PeriodicalId":49811,"journal":{"name":"Milan Journal of Mathematics","volume":"20 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Automorphisms and Twisted Forms of Rings of Invariants\",\"authors\":\"János Kollár\",\"doi\":\"10.1007/s00032-024-00403-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Let <span>\\\\(G\\\\subset \\\\textrm{GL}_n(k)\\\\)</span> be a finite subgroup and <span>\\\\(k[x_1,\\\\dots , x_n]^G\\\\subset k[x_1,\\\\dots , x_n]\\\\)</span> its ring of invariants. We show that, in many cases, the automorphism group of <span>\\\\(k[x_1,\\\\dots , x_n]^G\\\\)</span> is <span>\\\\(k^\\\\times \\\\)</span>.</p>\",\"PeriodicalId\":49811,\"journal\":{\"name\":\"Milan Journal of Mathematics\",\"volume\":\"20 1\",\"pages\":\"\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-07-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Milan Journal of Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00032-024-00403-x\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Milan Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00032-024-00403-x","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Automorphisms and Twisted Forms of Rings of Invariants
Let \(G\subset \textrm{GL}_n(k)\) be a finite subgroup and \(k[x_1,\dots , x_n]^G\subset k[x_1,\dots , x_n]\) its ring of invariants. We show that, in many cases, the automorphism group of \(k[x_1,\dots , x_n]^G\) is \(k^\times \).
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