In mathematics, the Cayley plane (or octonionic projective plane) OP2 is a projective plane over the octonions.[1] It was discovered in 1933 by Ruth Moufang, and is named after Arthur Cayley (for his 1845 paper describing the octonions).
As a symmetric space, the Cayley plane is 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). As a homogeneous space it is also the quotient of a noncompact form of the group E₆ by a parabolic subgroup P1.
In the Cayley plane, lines and points may be defined in a natural way so that it becomes a 2 dimensional projective space, that is, a projective plane. It is a non-Desarguesian plane, where Desargues' theorem does not hold.