High Quality Content by WIKIPEDIA articles! In mathematics, quaternionic projective space is an extension of the ideas of real projective space and complex projective space, to the case where coordinates lie in the ring of quaternions H. Quaternionic projective space of dimension n is usually denoted by Hpn and is a closed manifold of (real) dimension 4n. It is a homogeneous space for a Lie group action, in more than one way. Its direct construction is as a special case of the projective space over a division algebra. The homogeneous coordinates of a point can be written [q0:q1: ... :qn] where the qi are quaternions, not all zero. Two sets of coordinates represent the same point if they are 'proportional' by a left multiplication by a non-zero quaternion c; that is, we identify all the [cq0:cq1: ... :cqn]. In the language of group actions, HPn is the orbit space of Hn+1-(0, ..., 0) by the action of H*, the multiplicative group of non-zero quaternions.

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