Gyrogroups in Projective Hyperbolic Clifford Analysis
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Using the projective hyperbolic model in Clifford analysis we show that different velocities in special relativity theory (non-standard velocities, coordinate velocities and proper velocities) corresponds to taking different realizations of the hyperbolic geometry in the projective model. A full description of the changes is given, together with a proof of the isomorphism of the related gyrogroup structures (Möbius, Einstein, and proper velocity gyrogroups).
KeywordsGyrogroups Einstein addition Möbius addition proper velocity addition Lorentz group
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