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There is also a construction of '''H'''''P''<sup>''n''</sup> by means of two-dimensional complex subspaces of '''C'''<sup>2''n''</sup>, meaning that '''H'''''P''<sup>''n''</sup> lies inside a complex [[Grassmannian]].
==Infinite-dimensional quaternionic projective space==
The space <math>\mathbb{HP}^{\infty}</math> is rationally K(Z,4) (cf. [[K(Z,2)]]). See [[rational homotopy theory]]. Please expand.
==Projective line==
The one-dimensional projective space over '''H''' is called the "projective line" in generalization of the [[complex projective line]]. For example, it was used (implicitly) in 1947 by P.G. Gormley to extend the [[Mobius group]] to the quaternion context with "linear fractional transformations". See [[inversive ring geometry]] for the uses of the projective line of the arbitrary [[ring (mathematics)|ring]].
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