{"title":"中的不变量的限制定理和幂零元素","authors":"A. Premet","doi":"10.1070/SM1992V073N01ABEH002538","DOIUrl":null,"url":null,"abstract":"The ring of invariant polynomial functions on the general algebra of Cartan type is described explicitly. It is assumed that the ground field is algebraically closed and its characteristic is greater than 2. This result is used to prove that the variety of nilpotent elements in is an irreducible complete intersection and contains an open orbit whose complement consists of singular points. Moreover, a criterion for orbits in to be closed is obtained, and it is proved that the action of the commutator subgroup of the automorphism group in is stable.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"37 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1992-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"33","resultStr":"{\"title\":\"THE THEOREM ON RESTRICTION OF INVARIANTS, AND NILPOTENT ELEMENTS IN\",\"authors\":\"A. Premet\",\"doi\":\"10.1070/SM1992V073N01ABEH002538\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The ring of invariant polynomial functions on the general algebra of Cartan type is described explicitly. It is assumed that the ground field is algebraically closed and its characteristic is greater than 2. This result is used to prove that the variety of nilpotent elements in is an irreducible complete intersection and contains an open orbit whose complement consists of singular points. Moreover, a criterion for orbits in to be closed is obtained, and it is proved that the action of the commutator subgroup of the automorphism group in is stable.\",\"PeriodicalId\":208776,\"journal\":{\"name\":\"Mathematics of The Ussr-sbornik\",\"volume\":\"37 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1992-02-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"33\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics of The Ussr-sbornik\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1070/SM1992V073N01ABEH002538\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics of The Ussr-sbornik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1070/SM1992V073N01ABEH002538","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
THE THEOREM ON RESTRICTION OF INVARIANTS, AND NILPOTENT ELEMENTS IN
The ring of invariant polynomial functions on the general algebra of Cartan type is described explicitly. It is assumed that the ground field is algebraically closed and its characteristic is greater than 2. This result is used to prove that the variety of nilpotent elements in is an irreducible complete intersection and contains an open orbit whose complement consists of singular points. Moreover, a criterion for orbits in to be closed is obtained, and it is proved that the action of the commutator subgroup of the automorphism group in is stable.
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