{"title":"E8的一个八元构造与李代数幻方","authors":"Robert A. Wilson, Tevian Dray, Corinne A. Manogue","doi":"10.2140/iig.2023.20.611","DOIUrl":null,"url":null,"abstract":"We give a new construction of the Lie algebra of type $E_8$, in terms of $3\\times3$ matrices, such that the Lie bracket has a natural description as the matrix commutator. This leads to a new interpretation of the Freudenthal-Tits magic square of Lie algebras, acting on themselves by commutation.","PeriodicalId":36589,"journal":{"name":"Innovations in Incidence Geometry","volume":"27 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":"{\"title\":\"An octonionic construction of E8 and the Lie algebra magic square\",\"authors\":\"Robert A. Wilson, Tevian Dray, Corinne A. Manogue\",\"doi\":\"10.2140/iig.2023.20.611\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We give a new construction of the Lie algebra of type $E_8$, in terms of $3\\\\times3$ matrices, such that the Lie bracket has a natural description as the matrix commutator. This leads to a new interpretation of the Freudenthal-Tits magic square of Lie algebras, acting on themselves by commutation.\",\"PeriodicalId\":36589,\"journal\":{\"name\":\"Innovations in Incidence Geometry\",\"volume\":\"27 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-09-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"9\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Innovations in Incidence Geometry\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2140/iig.2023.20.611\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Innovations in Incidence Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/iig.2023.20.611","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
An octonionic construction of E8 and the Lie algebra magic square
We give a new construction of the Lie algebra of type $E_8$, in terms of $3\times3$ matrices, such that the Lie bracket has a natural description as the matrix commutator. This leads to a new interpretation of the Freudenthal-Tits magic square of Lie algebras, acting on themselves by commutation.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
