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 Möbius group to the quaternion context with "linear fractional transformations". See inversive ring geometry for the uses of the projective line of the arbitrary ring.
From the topological point of view the quaternionic projective line is the 4-sphere, and in fact these are diffeomorphic manifolds. The fibration mentioned previously is from the 7-sphere, and is an example of a Hopf fibration.
Read more about this topic: Quaternionic Projective Space
Famous quotes containing the word line:
“Next to the originator of a good sentence is the first quoter of it. Many will read the book before one thinks of quoting a passage. As soon as he has done this, that line will be quoted east and west.”
—Ralph Waldo Emerson (1803–1882)