{"title":"Eine kennzeichnung der oktavenebene","authors":"Hermann Hähl","doi":"10.1016/S1385-7258(87)80004-5","DOIUrl":null,"url":null,"abstract":"<div><p>We consider partitions of ℝ<sup>16</sup> into pairwise complementary 8-dimensional subspaces whose union covers ℝ<sup>16</sup> (or, equivalently, fiberings of %plane1D;4AE;<sup>15</sup> by great 7-spheres). It is shown that if such a partition is (globally) invariant by a closed subgroup of GL<sub>16</sub>(ℝ) locally isomorphic to SO<sub>7</sub>(ℝ,1), then it is linearly equivalent to the classical Hopf partition corresponding to the Cayley numbers %plane1D;4AA;, namely the system of lines through the origin in the affine Cayley plane over %plane1D;4AA;.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"90 1","pages":"Pages 29-39"},"PeriodicalIF":0.0000,"publicationDate":"1987-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(87)80004-5","citationCount":"8","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indagationes Mathematicae (Proceedings)","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1385725887800045","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 8
Abstract
We consider partitions of ℝ16 into pairwise complementary 8-dimensional subspaces whose union covers ℝ16 (or, equivalently, fiberings of %plane1D;4AE;15 by great 7-spheres). It is shown that if such a partition is (globally) invariant by a closed subgroup of GL16(ℝ) locally isomorphic to SO7(ℝ,1), then it is linearly equivalent to the classical Hopf partition corresponding to the Cayley numbers %plane1D;4AA;, namely the system of lines through the origin in the affine Cayley plane over %plane1D;4AA;.
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