{"title":"EIII 型对称空间的几何学","authors":"V. Petrov, A. Semenov","doi":"10.1090/spmj/1789","DOIUrl":null,"url":null,"abstract":"<p>Atsuyama’s result on the geometry of symmetric spaces of type EIII is generalized to the case of arbitrary fields of characteristic not 2 or 3. As an application, a variant of the “chain lemma” for microweight tori in groups of type <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper E 6\"> <mml:semantics> <mml:msub> <mml:mi>E</mml:mi> <mml:mn>6</mml:mn> </mml:msub> <mml:annotation encoding=\"application/x-tex\">E_6</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is proved.</p>","PeriodicalId":51162,"journal":{"name":"St Petersburg Mathematical Journal","volume":"108 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2024-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Geometry of symmetric spaces of type EIII\",\"authors\":\"V. Petrov, A. Semenov\",\"doi\":\"10.1090/spmj/1789\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Atsuyama’s result on the geometry of symmetric spaces of type EIII is generalized to the case of arbitrary fields of characteristic not 2 or 3. As an application, a variant of the “chain lemma” for microweight tori in groups of type <inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper E 6\\\"> <mml:semantics> <mml:msub> <mml:mi>E</mml:mi> <mml:mn>6</mml:mn> </mml:msub> <mml:annotation encoding=\\\"application/x-tex\\\">E_6</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is proved.</p>\",\"PeriodicalId\":51162,\"journal\":{\"name\":\"St Petersburg Mathematical Journal\",\"volume\":\"108 1\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-01-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"St Petersburg Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1090/spmj/1789\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"St Petersburg Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/spmj/1789","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Atsuyama’s result on the geometry of symmetric spaces of type EIII is generalized to the case of arbitrary fields of characteristic not 2 or 3. As an application, a variant of the “chain lemma” for microweight tori in groups of type E6E_6 is proved.
期刊介绍：
This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.
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