百度标志

Indagationes Mathematicae (Proceedings) Pub Date : 1987-03-30 DOI:10.1016/S1385-7258(87)80004-5

Hermann Hähl

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引用次数: 8

摘要

我们考虑将一个空间划分为若干对互补的8维子空间，它们的并集覆盖了一个空间(或者，等价地，%plane1D;4AE;15的大7球的纤维)。证明了如果这样的划分是局部同构于SO7(1,1)的GL16(l)闭子群的(全局)不变量，则它线性等价于经典的Hopf划分对应于Cayley数%plane1D;4AA;，即在%plane1D;4AA;上经过仿射Cayley平面上的点的直线系统。

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Eine kennzeichnung der oktavenebene

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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Indagationes Mathematicae (Proceedings)

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