Cayley plane

（重定向自Cayley projective plane）

In mathematics, the Cayley plane (or octonionic projective plane) P(O) is a projective plane over the octonions. It was discovered in 1933 by Ruth Moufang, and is named after Arthur Cayley (for his 1845 paper describing the octonions).

More precisely, there are two objects called Cayley planes, namely the real and the complex Cayley plane. The real Cayley plane is the symmetric space F₄/Spin(9), where F₄ is a compact form of an exceptional Lie group and Spin(9) is the spin group of nine-dimensional Euclidean space (realized in F₄). It admits a cell decomposition into three cells, of dimensions 0, 8 and 16.

单词	Cayley projective plane
释义	Cayley projective plane 英语百科 Cayley plane （重定向自Cayley projective plane） In mathematics, the Cayley plane (or octonionic projective plane) P(O) is a projective plane over the octonions. It was discovered in 1933 by Ruth Moufang, and is named after Arthur Cayley (for his 1845 paper describing the octonions). More precisely, there are two objects called Cayley planes, namely the real and the complex Cayley plane. The real Cayley plane is the symmetric space F₄/Spin(9), where F₄ is a compact form of an exceptional Lie group and Spin(9) is the spin group of nine-dimensional Euclidean space (realized in F₄). It admits a cell decomposition into three cells, of dimensions 0, 8 and 16.
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