On a quaternionic analogue of the cross-ratio (Q691051)

The first interesting result is given in Theorem 8, where the authors establish that for given two quadruples of distinct points there exists a fractional linear transformation which transforms the first quadruple into the second quadruple iff both quadruples have same cross-ratio. A second interesting result is given in Proposition 10, where the authors prove that for the fixed images of three points under all fractional transformations the set of the images of a fourth point is either a 2-sphere, or a 2-plane, or a single point. Some other assertions about mapping spheres into spheres of the same dimensions are given.