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On a quaternionic analogue of the cross-ratio. (English) Zbl 1257.15014

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.

MSC:

15A66 Clifford algebras, spinors
15A04 Linear transformations, semilinear transformations
51B10 Möbius geometries
15B33 Matrices over special rings (quaternions, finite fields, etc.)
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References:

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