{"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":null,"pages":null},"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}
引用次数: 9
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.
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